Yep, Dan nailed it. In my opinion, anyone who wants putting reduced or eliminated from the game is scared of missing putts. Or put another way, anyone capable of controlling the ball on a variety of shot shapes and doing it consistently day in and day out is perfectly capable of learning to putt well. Maybe not every touring pro can putt like Ben Crenshaw but not every touring pro hits the ball like Ben Hogan either.
The fact is that in the game's current (and traditional) form ball striking matters a lot. A pretty swing may not matter and the "best swing" by some abstract criteria does not guarantee the "best ballstriking". But hitting the ball far and sure results in lower scores.
When people say for instance that the PGA Tour is basically a putting contest, what they're really observing is that when you have a tournament field in which every single player is capable of striking the ball effectively the difference between first place and fifth or tenth place will be determined by putting. However, that is not the same as saying that putting is the majority of game. Putting is the majority of the difference between one good ballstriker and the next.
To use the Tom Watson example, he might be wild at times but he is one hell of a ballstriker by any standards other than Johnny Miller's or Ben Hogans. He knocks the crap out of the ball and can almost always find it. And he can play all the shots, albeit slightly less effectively than the best shotmakers who have ever lived.
It's a pipe dream to imagine a game where literally all that matters is controlling the ball on full-swing shots. It may be an interesting speculative exercise to try and design a game where Ben Hogan wins every single time he plays against someone who is "only" 99.99999% as skilled at full-swing ball control as Hogan. But for an actual game that engages millions of people and makes for compelling theater when played at the highest level the traditional game including chipping and putting works well. Yes, it may be that Ben Hogan can't win every time against some 2% worse at ballstrking who's a great putter. But it's still a fair contest and a fascinating game.
The "best" game IMO is one where a variety of physical skills and a variety of mental skills matter to the outcome. I think golf does that as well as any game I know of. Anyone who wants to reduce it to full shots wants to play a less interesting and meaningful game. And anyone who thinks the necessity of putting the ball into a very small target in some way detracts from the game is wishing to see the mental and emotional component of dealing with fear eliminated.