I guess it depends if you're interest is only in the courses, or in the culture as well. For the life of me, I can't understand being given the chance to immerse yourself in the "Muirfield" experience (substitute whichever other great UK club you want) and passing it up because all that matters is the course. I have been lucky enough to play a few of the world's great courses but my happiest memories of some aren't on the course. It's chatting with the head pro at CPC, then having a drink in the members bar afterwards, it's having a sandwich and a beer with my host at Kingston Heath, dinner and some really fine wine with my host at NSW. HCEG, Prestwick etc. allow you to enjoy the clubhouses and soak in the atmosphere. HCEG allow you to go out again and play alternate ball. Why not take that up, just for the sake of rushing to another course? Seems lunacy to me.
Makes total sense but do you actually know people that would pass up a full day at a Muirfield or a Cypress Point etc just to run off to play another 18? I can only think of maybe 2 people I know that are total golf course junkies that for example if skiers would have as a goal each and every day to log as many vertical feet as humanly possible no matter where they were skiing. Same essence really don't you think?
However, in the rare chance you are invited for the full whammy like you are suggesting even these guys that try to make every day of a trip, your 100 hole hike still wouldn't pass up what you are suggesting here.
I'm definitely guilting of having some crazy trips where I wanted to see as many courses as possible during a 2 week period for example, and those even included 54 hole days of walking 3 rounds. Usually those were only in the UK actually, and I wasn't being invited for full days at one of the famous places but more trying to see as many second tier (matter of opinion) courses as possible. Example would be playing, West Cornwall at 7 am, Perranporth after, having lunch at Trevose then playing a final 18 at Trevose on a beautiful afternoon. Seems crazy but was a really relaxed and enjoyable day even though I had to play West Cornwall alone which I normally don't love to do. In retrospect that was smart and way better than not seeing it at all as I would of missed out big time on a course I would of otherwise not likely travelled to see.
To Sean's point, I'd guess there aren't many courses I've been fortunate enough to see 10x myself. Heck even if you move the target to 5 that would be a smaller list but definitely not because I don't want to see them that many times, more because I've always wanted to see and study as much as possible, no matter what it all comes at great expense, both in time as well as money and travel costs. Makes sense that most of the courses you would see often are the ones that are closer to home. So I've seen courses like Utrecht De Pan, Royal Hague, Eindhovensche etc far more than most others courses that require a flight (which is almost everything). One thing absolutely true beyond a shadow of doubt is that the more I see a course (maybe a great course given my examples) the more I enjoy those courses. With every round I play on De Pan and at Royal Hague I like the courses more and more.
I have played a majority of my UK based golf in the shoulder season as well. I think it's my favorite time to travel and play there. March for example has always been great and yes, rough is down, less people, cheaper in all respects etc etc. Perhaps if we can even get to the UK later this year, the entire year will be like shoulder season. I really don't see too many American's jumping in planes in the next few months.