I read about 7 pages of the comments on this interesting topics, but not all (yet), so forgive me if I am duplicating something already said.
I voted that physical is most important to golf and I agree that it is most important by far. But,what good players view as physical, and I don't blame them for viewing this as such, can also largely be a mental issue for less skilled players. Things that are automatic for some, are not yet so for others and they need to think about those first, or they don't have a chance... I won't compare a player to another one, but instead one player (namely me) at different times, yet in similar conditions.
* Can someone tell me why I shot 75 and 111 less than a week apart (the 111 was on a more difficult course but still... it was the highest score in probably 8-10 years for me)? I was the same guy with the same physical abilities, but I made really poor choices, compounded errors with more errors and in the process lost the swing completely: shanks, tops, thins, etc... The silver lining was putting which is and remained my strength, even on that day...
* Can someone tell me why the first time my name was called on a tee box in an official Norcal (NCGA) tournament, I was shaking so badly, I nearly whiffed my drive which ended in a terrible spot, causing me to re-tee? It's some form of pressure, one I was totally unfamiliar with and which no longer affects me that badly. However, even at the highest level in golf, think Ryder Cup, the first tee shot is the most nerve wracking shot, for most people. You might say pressure is physical (tension, shaking, sweating, etc...), but it is controlled by the mind and by experience, so one can train for it, to some extent: breathing exercises, putting drills that force you to hole out x shots in a row or you start from scratch, playing worst ball with oneself, for example...
* Can someone tell me why in casual rounds and less so in competitive rounds, I sometimes forget my pre-shot routine and don't put myself behind the ball and then step in, but rather just step in and hit a great shot, 10 degrees offline to the left? Lack of focus and/or discipline, which is a mental error, leading to a physical one (being lined up wrong)
* Can someone tell me why, all of sudden, I completely lost any ability I previously had to hit fairway woods (there is another thread in "Instruction and Playing Tips" about this? I think I finally got it back, and while the practical cause is physical, the real root of the problem is mental. Not checking the ball position, hanging back because of it and losing balance (to my heels) in the process. All physical problems that can be overcome by an assertive mind.
Also, what about the power of visualization? Look at Jason Day actively and consciously closing his eyes prior to any swing. Also, do you see in your mind the line a well struck putt is going to take? I do, and unless my read is completely off (it happens once in a while, or the putt flattens at the hole and I didn't read that), for the most part that's what happens.
There is no doubt that our conscious and unconscious mind drives all physical activity and perhaps we qualify everything unconscious as physical and the swing certainly is too fast to consciously drive it in its minute details, but the conscious mind also has a role in controlling the outcome. YMMV.