Even if we drastically limit the scaling of attack bonuses, I want my fighter to have bigger numbers as he levels up because of what it represents in the game world. If a starting character in plate mail and a shield has 20 AC, then a low-level fighter doesn't have a great chance of injuring him. The playtest shows us a fighter with a +6 attack bonus, so he only has a 35% chance of hitting. By the time the fighter is high-level enough to slay dragons, I expect that he has a much greater chance of carving through a low-level knight's armor. At the least, I'd expect an 85% chance of piercing the armor.
If you're worried about AC getting too high, you wouldn't actually need to boost it from leveling. You could keep AC static (so a high level fighter would have 20 AC and a low-level fighter would as well) while gradually improving attack bonus (perhaps +1 per three levels for those leery of attack boosts). Thus, a level 20 fighter would have an attack bonus of +12. That would give him an entirely reasonable 65% chance of hitting AC 20, which I feel is not at all unreasonable.