The TWF fighter does less damage than a two-handed fighter on a single attack action (about 35% less), but virtually ties with a full attack action. Letting the TWF fighter always get his full attack damage significantly unbalances the equation in the other direction.

The thing is, whichever configuration you take, you can work on infinitely twinking it out. Two-weapon fighting is better when you want many more attacks. Being a rogue with sneak attack is the number one example of this. Or if you bleed per attack (like with Bloody Assault). Or use poison. Or use the various critical effects from the critical feats. Or want to use some of those attacks for trip/disarm/sunder attacks. There's a bunch of ways to increase your TWF damage by stacking "per hit" things on top.

Two-handed is better when something has DR or you're only getting one attack action in. Per-attack damage plusses and minuses and additional conditions affect a two-weapon fighter much more than a two-handed fighter - a "bard bonus" is multiplied in value by number of attacks. And as you note, you have to get a full attack to get those other attacks... But that's the same thing with a L11 two-handed fighter, they lose out on a lot of attacks when they can't stick and hit.

A straight fighter will do more dps in an abstract sense with a two-handed weapon than two-weapon fighting, if all he does is straightforward hitting without any other interesting feats. But if you change the TWF rules, your player is just going to turn around and layer the other TWF twinks on top and suddenly it's the more powerful thing, and you have to start worrying about your two-hander player... Because he who inflicts the most damage wins the game, apparently.

Also, there's a difference between optimization and real play. Real adventurers find gear, they don't "have 32000 to spend on it." I've played and GMed a lot of Pathfinder, and players have run and enjoyed two-weapon characters as much as two-hander characters. (Sword and board, however, sucks.)

Since the peanut gallery demands "math," here's some reasonably maxed out L11 characters, using all the Paizoey goodness. Each has more special abilites than one can reasonably enumerate, but I tried to stick to "jack up the numbers" options as much as possible. Full builds are below, but the relevant stuff here is that:

• 2HGuy, attack action: +23 (4d6+29/19-20 plus 1d6 fire plus 1d6 cold) 19-20 x2 - power attack, overhand chop is giving double STR to damage, vital strike, furious focus
• 2HGuy full attack: +23/+15/+10 (2d6+25/19-20 plus 1d6 fire plus 1d6 cold, 2d6+29 for attacks 2 and 3 from backswing) 19-20 x2
• 2WFGuy, attack action: +15 (1d6+15/17-20 plus 1d6 fire)/+15 (1d6+12/17-20 plus 1d6 cold) 17-20 x2 - two attacks from Doublestrike, piranha strike is like Power Attack for Dex, if he hits with both then 1d10+1 rend, if he crits +2d6 bleed, agile weapon enhancement gives +dex to damage
• 2WFGuy, full attack: +17/+12/+7 (1d6+17/17-20 plus 1d6 fire)/+17/+12/+7 (1d6+14/17-20 plus 1d6 cold) 17-20 x2, if he hits with both then 1d10+(1.5x Strength modifier) rend, if he crits +2d6 bleed, agile weapon enhancement gives +dex to damage, +2/+2 during full attack from twin blades, and also +4 AC bonus from two-weapon defense and defensive flurry)

Versus let's say AC 25, the average DPS (including crits and rend) for each is:

• 2HGuy, attack action: 55.67 (plus maybe shaken)
• 2HGuy, full attack: 87.06 (plus almost guaranteed shaken)
• 2WFGuy, attack action: 35.55 (plus two points of bleed)
• 2WFGuy, full attack: 81.80 (plus 5 points of bleed ongoing)

So yes obviously, in high mobility situations the 2WF guy loses out (though he does get two attacks, not one, from his archetype), but he's pretty much neck and neck in a full attack situation, any slight change to any of these numbers makes the winner of the full attack follies go back and forth. Both these characters have loads of other fun stuff to do, they have more feats than they know what to do with. The TWF guys is obviously much tighter on feats and stuff. Keep in mind this is a straight fighter compare, and there's other ways to fill out TWF and all those rogues with sneak attack can stack a lot of damage on... Go look at some build guides and there's plenty of L11 twf builds out there that do a lot more than this.

Does the TWF guy lose? Yes. But the question is, "is the answer to let him have his 81-point full attack with a standard action?" The answer to that is no, it unbalances it back the other way.

Full builds

Because everyone has stat boost items I usually don't add them, but in this case I decided to make up the wealth differential caused by the weapons with a +4 belt of strength.

2HGuy

Human (Kellid) Fighter (Two-Handed Fighter) 11 (Pathfinder RPG Advanced Player's Guide 0)
N Medium humanoid (human)
Init +1; Senses Perception -1

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Defense

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AC 11, touch 11, flat-footed 10 (+1 Dex)
hp 114 (11d10+44)
Fort +10, Ref +4, Will +2

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Offense

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Speed 30 ft.
Melee +2 cruel flaming frost greatsword +20/+15/+10 (2d6+25/19-20 plus 1d6 fire plus 1d6 cold)
Special Attacks backswing, overhand chop, piledriver, shattering strike, weapon trainings (heavy blades +2, pole arms +1)

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Statistics

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Str 24, Dex 13, Con 16, Int 9, Wis 9, Cha 9
Base Atk +11; CMB +15 (+19 bull rush, +18 sunder); CMD 29 (31 vs. bull rush, 32 vs. sunder)
Feats Bull Rush Strike^APG, Cornugon Smash, Dazing Assault^APG, Dreadful Carnage^APG, Furious Focus^APG, Greater Bull Rush, Horn of the Criosphinx, Improved Bull Rush, Power Attack, Pushing Assault^APG, Vital Strike, Weapon Focus (greatsword), Weapon Specialization (greatsword)
Skills Acrobatics +12, Intimidate +13
Languages Common, Hallit
Other Gear +2 cruel flaming frost greatsword, belt of giant strength +4, 150 gp

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Special Abilities

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Backswing (Ex) Attacks after the first in a full attack receive 2x STR bonus.
Bull Rush Strike Critical hit's confirmation roll is a Bull Rush maneuver check.
Cornugon Smash When you damage an opponent with a Power Attack, you may make an immediate Intimidate check as a free action to attempt to demoralize your opponent.
Dazing Assault (DC 21) -5 to all attacks and maneuvers but struck foes are dazed 1 rd (Fort neg).
Dreadful Carnage If you reduce an enemy to 0 or fewer HP, you can make an intimidate check to demoralize all enemies within 30' as a free action.
Furious Focus If you are wielding a weapon in two hands, ignore the penalty for your first attack of each turn.
Greater Bull Rush When bull rushing, foe's movement provokes AoO from your allies.
Horn of the Criosphinx Add 2x your Str bonus to damage rolls on charges while wielding a two handed weapon.
Improved Bull Rush You don't provoke attacks of opportunity when bull rushing.
Overhand Chop (Ex) Single attacks with two-handed weapons receive double STR bonus.
Piledriver (Ex) Standard action: attack with a two handed weapon, if successful, free bull rush or trip w/o AoO.
Power Attack -3/+6 You can subtract from your attack roll to add to your damage.
Pushing Assault If you are wielding a weapon in two hands, push the target 5' back instead of dealing power attack damage.
Shattering Strike +3 (Ex) +3 Sunder and damage vs. objects.
Vital Strike Standard action: x2 weapon damage dice.
Weapon Training (Blades, Heavy) +2 (Ex) +2 Attack, Damage, CMB, CMD with Heavy Blades
Weapon Training (Pole Arms) +1 (Ex) +1 Attack, Damage, CMB, CMD with Pole Arms

2WFGuy

Human (Kellid) Fighter (Two-Weapon Fighter) 11 (Pathfinder RPG Advanced Player's Guide 0)
N Medium humanoid (human)
Init +5; Senses Perception -1

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Defense

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AC 16, touch 15, flat-footed 11 (+1 shield, +5 Dex)
hp 114 (11d10+44)
Fort +10, Ref +8, Will +2 (+3 vs. fear)
Defensive Abilities bravery +3, defensive flurry

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Offense

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Speed 30 ft.
Melee +2 agile flaming cold iron shortsword +15/+10/+5 (1d6+15/17-20 plus 1d6 fire) and
   +2 agile frost mithral shortsword +15/+10/+5 (1d6+12/17-20 plus 1d6 cold)
Special Attacks doublestrike, improved balance, twin blades

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Statistics

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Str 13, Dex 20, Con 16, Int 9, Wis 9, Cha 9
Base Atk +11; CMB +9; CMD 27
Feats Bleeding Critical, Critical Focus, Double Slice, Greater Two-Weapon Fighting, Improved Critical (shortsword), Improved Two-Weapon Fighting, Piranha Strike, Two-Weapon Defense, Two-Weapon Fighting, Two-Weapon Rend, Weapon Finesse, Weapon Focus (shortsword), Weapon Specialization (shortsword)
Skills Acrobatics +16, Intimidate +13
Languages Common, Hallit
Other Gear +2 agile flaming cold iron shortsword, +2 agile frost mithral shortsword, 150 gp

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Special Abilities

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Bleeding Critical Critical Hits deal 2d6 bleed damage.
Bravery +3 (Ex) +3 to Will save vs. Fear
Critical Focus +4 to confirm critical hits.
Defensive Flurry +3 (Ex) +3 AC vs. melee when making a full-attack with both weapons.
Doublestrike (Ex) Standard action: Attack once with each weapon (normal two-weapon penalties).
Improved Balance -1 (Ex) Reduce the penalties for two-weapon fighting or count off-handed one-handed weapon as light.
Piranha Strike -3/+6 You can subtract from your attack roll to add to your damage with light weapons.
Twin Blades +2 (Ex) +2 to hit and damage when making a full attack with both weapons.
Two-Weapon Defense +1 to AC while wielding 2 weapons. +2 when doing so defensively.
Two-Weapon Rend Deal extra 1d10+(1.5x strength modifier) if you hit a foe with both main and off hand weapons.

The biggest reason I can think of is that Dex, along with Wisdom, is already at least on the border of being "too versatile," in the context of 3.5 and Pathfinder. While it's true that Rogue, for example, is a weak class in the core rules, it isn't due to the reliance on Dexterity.

In 3.5e and PF, Dexterity does these things:

• Determines your initiative. This ensures that Dexterity is at least marginally useful for every class in the entire game.
• Adds to your armor class, and more importantly, boosts your touch AC. Also good for everyone.
• Determines your to-hit with ranged weapons and finesse weapons.
• Determines your reflex save -- another one that's a little important for everyone, since the most common thing that invokes a reflex save is either a trap or an AoE attack, which everyone in the game is likely to be subject to at some point.
• Is the modifying attribute for a proportionally large number of skills relative to other attributes

This is also pretty much identical to the way that 5e handles Dexterity. So why does it work in 5e and not 3.5e and PF? There are some key differences:

• In 5e, touch AC is not a thing. This is important.
• Armor now has a strength requirement on it as you go heavier, as well as being much stricter about limiting Dex bonus to AC, meaning it's either impractical or pointless for most characters to stack a high Dex modifier with something like mithral full plate; heavy armors with improved Dex-to-AC bonuses.
• In 5e, modifiers aren't really a thing outside of your regular old Str/Dex + Proficiency bonus to attack. Magic items are also supposed to be harder to come by, although that can vary with your GM. Depending on whether you can get advantage or not, this might make it harder for you to accumulate the modifiers you want (advantage is supposed to be equivalent to about a +4 or +5 bonus, if I recall correctly)

In conclusion, it's clear that giving Dex the same functions as 5e would make it more powerful in the context of the rest of the rules in PF. I can't say for sure that it would break your game, since that mostly depends on what class the character in question ends up being. Balance in PF depends highly on the individual class.