This question has been rattling in my head for a few days (along with several other loose screws), and since nobody else seems to want to comment, I thought I'd throw out a few of them thar ideers..
Stuff that would stay the same
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1) The objective of the game (either one) is to get the ball into the hole in the fewer strokes. This doesn't change, it just changes how to add (total vs. hole-by-hole)
2) Technology of clubs and ball would have still evolved. We are hopelessly addicted to this game, and while a few will stand firm, nobody is looking for the game to get harder. New technology makes the ball go farther and straighter (sometimes). Fight technology all you want, but there has never been a technology regression (courses are a different story).
Stuff that would probably have changed
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1) As an architect, I would place a little more emphasis (if the land permitted) on placing risk-reward holes earlier in the round. Great finishing holes are often not used in match-play as the match has ended.
Thinking about this approach vs. some existing courses thought of as stroke-play courses, I find that some might also be good match-play courses (if #1 is actually a valid point). For example:
ANGC - #2, 3, 7, 8, 11, 12, 13, 15 would all come into play in most matches
2) There would be no need to place a "Par" rating on any hole. There would be no need for a course record, or debate if a 490yds hole is too difficult to be a Par4.
3) We'd probably enjoy the company we play with more, because "that slow guy" wouldn't hold us up as much in putts were conceded or he's out of the hole after going in the water. Or maybe we ought to just dump that guy instead....
4) We'd hopefully no longer have to hear Mike Tirico explain what "dormie" or "All Square" means on another broadcast. It's as bad a going to a Carolina Hurricanes game and having them explain icing or offsides to us.
With all that said, I can never see American golf going back to a match-play dominant mentality for the following reasons:
1) Match play doesn't give us great heroes or dominant figures. Looking back over the last 80+ years, only Hagen, Jones and Woods have been really dominant at match-play. Granted the PGA changed formats and things like US-Am weren't on TV or the WGC Match-Play didn't exist, but few Americans have ever had "great" Ryder Cup records.
2) We'd go crazy trying to compare players, especially if they rarely played against each other.