It'd be similar to NBA games morphing into nothing more than free-throw shooting contests. How many of the current players would remain in such a league? If there were any, you could count them on a couple of fingers.
There are guys who can drain 50 straight foul shots with regularity and are deadly accurate even from 3-point range. However, they have no prayer of even getting a shot off in the flow of an NBA game, and thus are of no use to those teams.
It's the same thing with all the putting superstars who would emerge. If they can't get themselves into birdie range on a PGA Tour course, their acumen with the blade is pretty much irrelevant.
But change the rules to where the contest is about nothing other than their specialty and it's a whole new ballgame. Dead-Eye Joes would start showing up from every direction on the compass.