First off, I'd say that if your going to do a feat for this, then make it a straight up bonus. Doing it by your BAB is just going to cause problems later on.
Second, I'd say if you want to encourage unarmored fighting, its better to simply create situations where that would be advantagous.
1) Have encounters during rest periods. By the book, most fighters aren't wearing their armor at night, or they get penalties in the morning.
2) Make armor unsuitable for some locations. Certains towns may say you can't bring armor into a town just as much as weapons. Or in certain weather, like lightning storms, wearing armor may be a bad idea.
3) Take away a player's armor for a time. Use a rust monster or what not to strip away armor. This is my least prefered method, I think it cause bad feeligns, but it is an option.
An unarmored fighter is just like a rogue, or a paladin, or a bard, these classes are VERY powerful in some instances: not so much in others. If these players feel they are getting hosed, give them some situations they can shine in.