Maybe some experts could chime in here.
I'm certainly not a golf handicapping expert, but I do have a non-trivial education in statistics, so I understand the math behind handicapping.
The current system, but selecting the lowest 8 scores instead of the average, rewards consistency,
not absolute skill. While you might think that targeting one standard deviation lower would reward 'good' days, since it's one standard deviation for everyone, it sort of doesn't matter except the optics of putting people 'above net par' whatever that means. Where it does matter is that a consistent player's off days will be closer to net par, all things equal, than an inconsistent player.
Where I think the math gets really challenging, is that it's built on the assumption that players have some sort of normal distribution in their rounds. The previous reasoning I've given is based on symmetric distribution, but I'm not entirely sure this would be the correct distribution, as a skewed distribution might map better to performance, or even a different distribution altogether, say, something
similar a Poisson distribution (note here that a Poisson distribution is inappropriate for golf scores, but I mean just generally, having a lower-bounded distribution seems very sensible). I think a multi-modal distribution would be something we should expect to account for different distributions of home, away, and competition results (which is effectively the point if this thread anyway).
How does the current system effect those alternative distributions? I'm not sure. I'd probably have to think about it quite a bit. The good news is that the USGA is now collecting data from all golfer via the GHIN app, which means this isn't a philosophical problem, because we can actually look at the distributions! We could even look at distributions of player distributions. This means that now is very much
not the time to stick to tradition for tradition's sake. We should be updating our handicapping systems using this data for create the results that we are looking for.
What we want from handicapping results is more of a philosophical question. It's one where I've argued here, and will continue to argue here, that
any handicapping system that does not strive to distribute victories equally across players makes no sense. I'm sure many folks would/will argue with me on this point, but I cannot understand any reasoning that says "we want to give weaker players a helping hand, but not an equal playing field." I could see why some people would
want skilled players to get more victories, but then why use the handicapping system at all. If it's a system we are all agreeing to use, it seems pointless to create one that does not aim to distribute victories to everyone in the room. Literally any "but I don't want to lose to someone who I'm better than" can be solved in that scenario with using a handicap percentage over a full handicap.
Where I think there is room for debate is whether and how we limit variance in results. I've discussed earlier that somewhat limiting variance probably makes sense if we want to distribute victories, because if variance isn't punished, we should expect the highest variance players to win much more often.