Weapon Finesse is still a Weak feat, so this makes it a bit more viable. Basicly, you're letting a character who is using an inferior weapon damage wise (a finesse weapon), and using a different stat to allow him to hit with it, and requiring he give up a feat, something that most characters don't get manny of anyway. And, since your dex is likely higher than your strength, you're still doing less damage, since you don't get as high a damage bonus, than if you had a high strength.
Now, I would adjust this so that Strength Penalties still apply. If you're realy worried, make it BAB +4, which means most people get it at 6th level. Seems fairly balanced at that point.
Also, don't forget, a warrior with a low strength still can't carry much either, so there is still a use for strength.