Someone said that 'enabler' feats like Weapon Finnese and the like would be auto-given to classes who would use them (like the rogue.)
But honestly, I see no reason why STR would be the only ability to add to your meele attack bonus. Some people say that it helps you "pass through armor," but surely that is not the only way to help you hit more often. I for one prefer gamism to simulation, within reason, and as such, I am more open to new mechanical options.
An ability score strongly tied to any class makes sense to me to add to hit: STR- as mentioned before, DEX- quickness and mobility allow you to strike accurately, CON- uhhh... ok that dosn't make sense, INT- detect and aim for weak part of enemy defenses, WIS- intuition and body language guide your attacks, CHA- dosn't really make sense, but I could see it working for a Paladin.
This of course would only be the case with weapons the character is proficient with. If the ballet dancer is not proficient with the axe, then he wouldn't be able to use his Dex mod with it. However, a balled dancer proficient with axes could be a deadly enemy.