As a way to make it viable, and to make dex bills actually worth considering again, I suggest that a finessible weapon, when coupled with the feat itself, receives a bonus to attack speed.
no, they wont be doing more damage per hit, but they will definitely be doing more hits. It would almost make more sense for the bonus to be different for each weapon, as i dont see how anyone can swing a rapier faster than a dagger.
So, for example (i know these arent the only finesse weapons)
Rapier: Bonus 10% attack speed when useing weapon finesse.
Shortsword: Bonus 15% attack speed when useing weapon finesse.
Dagger: Bonus 20% attack speed when useing weapon finesse.
EDIT: After re-reading the feat description, my suggestion must also include that when useing weapon finesse and a finesse weapon, your dex modifier is what determines your attack roll regardless of which is higher between dex and str.
Honestly allowing somone to have weapon finesse and still use str modifier for light weapons is just plain silly. It's more a waste than power critical or skill focus swim, so this addition to my proposal shouldnt be seen as going to far.