Bo, your primary argument seems to be that an P2 is a P2 is a P2. If this is so, then the local/visiting status of an accident pilot should be immaterial. And if pilots with higher ratings are also having incidents, this wouldn’t seem to bode well for H2s in those same conditions.
The historical basis of the signoff is that Crestline/Marshall used to be an H2 site (this was pre-PG). And it certainly can be. It can be a wonderful resource for novice pilots to get some airtime and become not-so-novice pilots.
The problem was that freshly-minted H2s would come and get into various problems. One memorable one, which sort of brought things to a head, was one that crashed into the tower by launch. Fortunately, it wasn’t a fatality, but it did break some antennas. This was also before Rob started keeping track of incidents with red dots and yellow dots, so it’s not in that database.
So we changed to H3, with an H2 signoff, to try to cut down on unsupervised flights by pilots with — not so much a lack of skill — but a lack of judgement. The five approaches into the LZ was added when we moved to the current LZ from Pinecrest, mostly because of overshoots, but partially to help with separation of slow from fast traffic, as PGs were starting to be a thing.
The time of day restriction originally only applied during Daylight Savings Time. In the winter, the sun was generally low enough that conditions weren’t that strong.