mutants-and-mastermindspowers
Since Enhanced Trait costs the same as the base trait, won't allow you to go over the power level limit, and adds several drawbacks (like it being nullified), I don't really understand why anyone would get it over just increasing the trait.
What is it good for?
Honestly, I'm not truly convinced that there is a problem. As you say, the 'problem' only appears as a significant setback with extreme tradeoffs. A character at PL10 who is at 16 attack/4 damage is not someone who is supposed to be going toe-to-toe with equivalent PL opponents.
People who are attack shifted should have a thematic reason for the shift. This theme should also indicate how they can rectify the situation.
Batman, for instance, is attack-shifted. He compensates by having a versatile selection of attacks with varied defenses. He also uses things like Set-up and Teamwork to benefit other heroes (such as those unfortunate bricks who are heavily damage-shifted but can't land a blow on an agile opponent).
That said, the suggestions you give for 'fixing' this don't seem to be good fixes for me. Both are variations of having your cake and eating it too by letting accurate attacks deal more damage. Autofire, for instance, means that putting 2 points into your attack is strictly better than putting 2 points into your damage: you are both 10% more likely to hit AND your attacks do 5% more damage.
Mutants & Masterminds is a comic book-inspired Super Hero game. Not all characters are supposed to be able to do everything. If you are being presented with a foe that your typical attacks can't hurt, consider what your favorite super hero does in his/her comic when confronted with that situation. Spider-man doesn't complain that it isn't fair his punches can't hurt Rhino, he uses his combat advantages to make him charge a power transformer or get stuck in a wall and webs him in place.
You don't need a mechanical 'fix' for a 'problem' that is intentionally built into the system. If you don't want to be faced with a situation where your character can't damage his foe, don't play a significantly attack-shifted character.
You can mathematically analyze mechanics to your hearts content, but if you are doing that at the expense of a fun game, you're missing the point.
Addendum: One thing that attack-shifted people have going for them is MultiAttack. I was reminded of this by this question. Multiattack adds +1pp/rank to the cost of an Effect, and allows you to do additional damage to a single target if you exceed their defense (+2 or +5, depending on how much you beat them by). You still have to be able to damage them with the attack (so you have to beat their Impervious threshold) to do so, but it addresses the tradeoff issue in much the same way as Autofire does. It also gives you a few other combat options (hitting multiple people for a minor attack penalty or giving an ally a Defense bonus).
Edit: In response to this being called a 'poor answer that dismisses the question', allow me to elaborate on my reasoning for being 'dismissive':
Attack is already cheaper to buy than Damage. Yes, if you just pump up your Str, you get melee attack and damage. But there's easier ways to buy your attack up. Most simply, you can get +2 attack / 1 pp by buying your attack as a skill (Close Combat: Unarmed) with a narrow focus. So an attack-shifted person who meets his caps can (and typically does) have more pp left over to buy things with.
The question points out that critical hits, which always hit, are a huge problem for attack shifted people: 1/20 hits, the defender will always lose anyway. The question indicates that this will be an auto-hit with +5 damage 1/20 times. Unfortunately, that's not right. This isn't always the case: critical hit must still exceed the targets Defense to get the +5 damage (or Alternate Effect). Of course, for a heavily damage-shifted character, one attack landing might be all they need.
The 'math' that is shown is overly simplified and the graphs are inconclusive. The graphs simply show numbers from -5 to +5, but don't indicate which direction the shifts go. They also assume two characters are simply standing and punching each other every round. Does this seem like something reasonable in a game?
The question, in my opinion, completely fails to demonstrate a real problem with the system. By narrowing it down to pure trade-offs and ignoring things like the fact that players typically have other party members assisting, the multitude of attack-boosting skills a teammate can have, and the many types of Effects that can render a character combat-ineffective without resorting to Damage, the question artificially narrows the system down to a single mechanic. The mechanic in question does have a bias, but the question neglects the many corrections for this bias which exist in the game.
The question seems to completely ignore any Effect other than damage. When simply hitting your target is enough (such as with a Chi attack resisted by Will - built as an Affliction with whatever penalties you like) being attack-shifted is purely better than being damage shifted.
Ultimately, the answer to this question is simple: work with your teammates to overcome your weakness. Watch an episode of Justice League where Batman and Superman work together. Watch Young Justice, and see what Robin does while Superboy is pummeling things. Watch Teen Titans and see why a young Nightwing is considered good enough to be on (and hell, LEAD) a team with a master of magic, a cyborg that can crush mountains, and an alien who can melt tanks from across the room.
When evaluating any system, you can't simply look at a single mechanic (in this case, trade-offs) - you have to consider the whole game.
The second part of your question, about Slam damage, has a canonical answer.
The Gamemaster may limit your base slam attack damage (before applying circumstance modifiers) by the series power level.
Example: Your hero flies into a foe, moving at speed rank 10. His unarmed damage (Strength) rank is only 2, so he uses his speed rank of 10 for the damage. Since he also moved his full speed to build up momentum, he increases his damage by +1 for a total damage rank of 11. If a base damage rank of 10 is too high for the series, the GM may impose a lower limit on his slam attack damage, applying the +1 modifier for the full speed move to the lowered rank.
So, in short, there's nothing guaranteeing you a chance to break PL, especially if you have a character built to avoid any of the damage from doing the attack.
As regards reaction "attacks" by linking it to movement, the onus is on the GM to police abusive builds like that.
The GM is the final arbiter as to whether or not a triggering circumstance is suitable for a particular effect in the context of the series. Caution should be used to keep this option from being abused.
Best Answer
First, because you can assign flaws and extras
Flaws reduce the cost of the power, and thus allow for a more efficient use of power points. For example, if I was making a character like Iron Man, I could give him a whole slew of Enhanced Trait powers representing the general superiority of wearing a suit like that, but then give them Removable 1 (among other things) to represent that the suit can be removed and the powers lost. Its used as a power and not as equipment in order to represent how core it is to the character. Iron Man's suit is a power, a kevlar vest is equipment. Limited is also a good power, Superman would likely have a whole slew of Enhanced Traits, but with Limited (Kryptonite) in there somewhere. And note, the Limited flaw has a fairly dramatic effect on the power cost.
Admittedly it doesn't look like there are that many extras that might work well. But the same concept applies, of allowing you to add interesting flair to the Enhanced Trait. Indestructible could at least mitigate a Removable trait, Innate prevents your concern with nullification. Subtle has interesting effects as well as it could cause a character that appears weak to be in fact be unnaturally strong, that sort of thing.
Obviously, it takes a good GM to properly handle the flaws on powers to prevent them from getting out of hand ("No, you cannot take Limited 1 (power does not work in space) for a game that will only take place in Seattle"), but results in fairly rewarding games if you can put interesting flaws in there.
Second, it allows it to be used as an Alternate Effect
This means you could have a sort of "dial" of powers that you can switch between while having an overall reduced cost than having each of them individually. You just have to accept you can't be both super strong and super agile at the same time. But you could say have something like Funnels from Gundam, that can defend you by deflecting incoming attacks (Enhanced Trait Dodge), but then can also be used as an attack. The trade-off is it can't attack and defend on the same turn.
Third, it allows for the use of descriptors with your powers
Your agility might be tied to water, and that might have very real affects on how your power interacts against someone who's power is say, based on fire. See M&M3e p.154 for more on that, its a whole part of the system.
Fourth, you can use Extra Effort to increase the magnitude of the power
(Thanks to @Sean Duggan for pointing this out) Per p. 19 of M&M3e, you can use Extra Effort to increase the rank of a non-permenant power by one, until the start of the next round. This also bypasses normal PL limits, so in theory you could use Extra Effort to increase an Enhanced Trait Fighting. That would improve your Parry as well as Melee Attack accuracy.
Fifth, your GM may impose limitations on buying abilities and other traits
For example (p.55 M&M3e), 7 is often considered the "peak of human achievement," and some GMs may require that a human character in a M&M game at most only have 7 in an ability (and thus anything beyond that is a power).