Bart:
I have to agree with Ryan about the ninth hole at Arcadia. It's the most spectacular hole on the course, but maybe the worst hole, too. That 190-yard tee is not a 4-iron on a nice summer day with the wind blowing from the north; it's still a wood for most golfers. And if you play for the shorter carry, there are two VERY deep bunkers blocking the entrance to the putting surface. And then the putting surface slopes away from the bunker for 30-40 feet, so a ball which just makes the carry shoots on away to the back of the green. Playability is not the hole's strong point.
Matt:
Seems to me there are a lot more very-long par-3's being built now, on public and private courses alike. Ten or twenty years ago, nobody wanted to build them. But many of the holes you have cited are at altitude, so they don't really play all that long ... the Black Mesa hole is just a 200-yarder plus altitude, isn't it? I can't remember what club I hit there but it surely wasn't driver.
For myself, I can't say that I have used the concept more on private courses than on public layouts; we just haven't built as many public courses recently, period.
It is hard to include a 240-yard hole in a really windy places, because there are days when it won't be reachable at all, and most people are going to hate that. Pacific Dunes doesn't have a very long par-3, for that reason. I've still seen good players have to hit driver on #5, #10, and #17 depending on the day.