With the normal fighter builds found in the PHB, is there any weapon choice (hammers, light blade, heavy blade, axes, etc) that does statistically better damage based on weapon damage, power selection, and appropriate stat?
Yes, there is a good reason for feat prerequisites.
Two reasons, in fact:
To clarify by indicating what build a feat is intended for (a feat that boosts Lay on Hands usually requires that you have Lay on Hands)
To balance by forcing players to dedicate more resources in order to take a more powerful feat.
I suspect the reason you're surprised to encounter this is that by and large 4e feat prerequisites are for clarity: if there's a feat we want, we probably already qualify for it. (In previous editions of D&D prerequisites were much harsher and it was common to plan our characters around qualifying for certain feats.) It's surprising to find a feat we want that we can't take in 4e.
Mastery feats need to be balanced carefully:
Feats like the Mastery set can be very powerful: they double crit range from 1/20 to 1/10, and for a build that 'fishes' for critical hits that's pretty massive (other builds wouldn't be as impressed by it, but a feat's value shouldn't be based on its usefulness to a character that wouldn't take it anyway). Consider a burst/blast wizard who attacks an average of 4 targets each round: compared to a character with expanded crit who makes one attack in the same time, the wizard with expanded crit will deal maximum damage every 3 rounds instead of every 10. If he has specialized in making his criticals awesome, this is very powerful.
In order to allow such feats to exist without unbalancing the system 4e has imposed more stringent prerequisites to take them. But...
The requirements really aren't that harsh:
Prerequisite: 21st level, Dex 15, Int 21, Wis 15, wizard
At level 21 two of a character's abilities can have increased by +6, and the other four abilities have increased by +2. This means that for Wizard Implement Expertise I can start with (before racial modifiers, assuming I take a race with +Int) a 13 Int, Dex, and Wis to qualify at 21 without focusing on either of those secondary stats or having racial bonuses to them. Roughly two out of every three wizards will have focused on at least one of them, and it's important to remember that the 4e stat generating system makes it impossible for me to start with less than a 14 in at least one stat.
A player who wants the feat should have been considering it ahead of time and planned accordingly--but even a wizard who hadn't planned to get the feat is likely to qualify. (If I want it so bad anyway, I've got two +1 stat bumps at 24 and 28 to bring my 11 up to a 13 and still enjoy the feat for the last three levels of the game.)
Sure, change it if you like.
The phrase "feat tax" gets thrown around a lot. It seems to mean that there are specific feats I need to take in order to not be a burden on my party. I generally disagree with this idea because it presupposes a specific kind of character optimization which is just one style of play rather than a philosophy of the game design.
Feat slots are limited for a reason: to force choice. There are better and worse choices, though 4e has done a surprisingly good job of limiting downright awful choices. By lifting feat prereqs and granting free feats, your group would be saying these choices aren't part of the kind of game they want to play.
And if that's your party's play style, go for it: there's no wrong way to play the game provided everyone's safe and happy. But it's not the way the game was designed, and the game wasn't designed by accident (however much I joke about the adventure writers), so we're less surprised by mechanics like these if we understand the original philosophy behind them.
It really depends. for a cleric, they are functionally identical.
Here are the damage expressions:
Two hander: 2d6 + str
TWF: 1d6 + str, 1d6
Literally exactly the same when you factor in that your to-hit is going to be the exact same number for both. You only get your Divine strike (I think War domain gets that at 8 and 14 like the Life cleric does) on the first hit so that does favor TWF slightly at 8 and more at 14.
The next thing to look at is the action economy. TWF uses your bonus action every round. Whereas GWF leaves it free. You've got some bonus action spells you might want to use.
Lastly, there is feat selection. A melee cleric is MAD (Multiple Ability Dependent) so you might not want to actually pick up a feat and let both your stats run up to 20, but if you could settle for an 18 str, you might want to pick up the feat related to your fighting style. The GWF feat gives you extra attacks, but the TWF feat lets you wield one handed weapons rather than only light weapons and boosts your AC a bit.
Really, looking at the numbers, the decision is entirely up to you and how you want to play the character, they are quite similar. I give the damage edge to TWF, and the action economy edge to GWF. Ultimately though, at high levels, your cantrips might end up doing more damage than your weapon attacks anyways.