As characters and their powers progress... so do their damage output. The fighter's damage output increases in the sense that their BAB is high, so they get more multiple attacks... albeit at a lower BAB. The PRG further enhances this by adding in Weapon Training.
With Power Attack capped now, the fighter's damage output is limited, and the extra attacks from a high BAB don't help as much since they are less likely to hit.
I like the weapon training idea, but I'd like to throw out the following idea for discussion. Change weapon training so that it only affects damage. While using the same mechanics (choosing weapon groups, whose effects are cumulative in each weapon training selection), only allow the benefit to be for damage (and not the attack roll).
Start the Weapon training benefit at 1st level, and then increase it every 3rd level (i.e. 3rd, 6th, 9th...)
There are an adequate enough feats that can help the Fighter's attack bonus. (Not to mention that their BAB helps as well). I believe the Fighter's BAB really doesn't need a lot of help, where-as their damage output does. This proposed method would fix it, yet keeps the mechanics balanced.
I'd sort of like it if fighters could deal a whole bunch of damage with whatever weapon is at hand, and not have it tied to a specific weapon or groups. Maybe an untyped +1/2 class levels to all weapon damage.
With regards to specific weapons, Weapon Focus and Weapon Specialization desperately need to scale by BAB. Maybe the former is +1 to attack per +4 to BAB, etc. (+5 at BAB +20). This makes the fighter's feats as useful as the cleric's 1st level divine favor spell, instead of a pale, feat-devouring shadow of it.
Also -- and I personally think this would be fun at the table -- if you want to nerf the usefulness on crits slightly but really increase the glee of rolling a bunch of damage, give 'em a precision-based +1d6 damage (kind of like a sneak attack, but no need to flank or catch flat-footed) each time they get weapon training, instead of an untyped +1.