Patrick:
I think golf courses would be VERY different if there was no such thing as stroke play.
The two major differences would be:
a) The nature of hazards would be much more rugged, and
b) The level of conditioning would be less important and presumably less costly. I wonder if golf courses would have become backyards for housing estates at all, in these circumstances?
One could also argue that golf might be less popular in America, since you wouldn't have a game unless you had an opponent. But, hell, maybe then the American golf culture would be more like the Scots golf culture ... and that would be a thing of beauty.