Also, giving the +d6 (or whatever) bonus to an action with an AP steps on some of the paragon paths established. Rather than anyone and everyone getting more accurate with an AP, some heroes (such as Kensai) can reroll, while others do more damage, get better defenses, can also move, etc.
Not that I dislike another use of AP (I never played 3.x) but I can see why, given the specific uses for them in Paragon paths, the designers wanted to restrict the basic usage of Action Points to a specific single benefit which would not be duplicated in any Paragon path.
Also, our group (some of whom played 3.5, and some of whom did not) all love action points, and haven't even hit paragon play yet. They don't even consistently use them for an attack. Often they will use one after a big bold attack to take a Second Wind (so they attack, then heal, then get boosted defenses). Our wizard ran up to a gang of orcs, used Burning Hands on all of them to roast them, then used his action point to run back to the back of the party. Our rogue has used them to move and make a stealth check after an attack. I'd say we've used them just as much for a second move, or a Second Wind, as we've used them to attack.