Four pages in, I’ll just come out and say it. I don’t enjoy the concept of par. I think its utility as a way of keeping observers aware of where a golfer stands in an event is useful. But as a tool for organizing and characterizing holes? To me it seems antithetical to the variety required for a golf course to be interesting and fun. The formulaic needs of golfers is odd to me.
It is interesting to contemplate par and what it really means. Thinking of the Old Course, you've got 9, 10, 12, 18 at least are all really 3.5 par. Then on the other end you have 4 and 13 which are more like 4.5s. 17 is almost just a straight up 5, but we can lump it in with the 4.5s. Then the actual par 5s, depending on the wind, one of them (for the pros at any rate) is probably a 4.5 and the other a 5. So even though there are "only" two par 3s and two par 5s, the variation in hole length there is really pretty good. But it does seem kind of funky to put 9 and 17 in the same bucket of par 4.
But I think one thing that affects this discussion is par 3s are really either 3s or 3.5s. There are not really any 2.5 holes. Even a hole that's 100 yards is still going to average pretty close to 3. It's hard to get it up and down from 100 yards, even for the best in the world. Similarly, for the par 5s, those are either "easy", in which case they're more like 4.5s or they're difficult and are really 5s. I don't think there are any 5.5 holes out there. Or very few to speak of anyway. So par 3s get to be 3-3.5. 5s get to be 4.5-5 and par 4s have a much wider range of 3.5 to 4.5. Since lots of people like half par holes, the par 4s have an intrinsic benefit there.
The other thing is we've talked a lot about strategic holes/shots in this thread. I personally don't feel there's a whole lot of strategy to an approach shot. Not much beyond possibly which side of the hole do I want to miss on if I do miss. That might be a few yards one way or the other. I guess you might have a choice of whether to fly it or run it on, but these days, most people fly it on - certainly in my golfing circles. Tee shots are really where the strategy can come into play though. So par 3s I really don't think can manage much on the strategy side. They do though get to be played on some of the more extreme terrain (15 and 16 at CPC for example) and I do think frequently people count how pretty a hole is as a part of how good a hole is. I think it's pretty hard to come up with a par 5 that has good strategic options on both drive and second shot, so when someone does it, it stands out. I suspect that's a portion of how par 3s and par 5s wind up on best hole lists. Par 4s, you can build strategy in relatively easily (I assume anyway - I'm not an architect).