I don't disagree with you on this, I went to a private school. My only question is how many public schools have been able to do that and sustain it over the last 20 years? Other than the traditional powers... I would say an elite program is almost a yearly semifinalist. That's just my opinion though.
Here are the elite public programs I can think of off the top of my head.
MS
LWE
Cary
PR
Rochester
Lena Winslow
Batavia
East Side
Glenbard West(although they've been down recently)
I think there's a lot of other schools out there who have glimpses of being elite but if the talent isn't there it's just not sustainable. I'm thinking of the Lockports, York, Wheaton Norths, Warren, Palatine had back to back semifinalists even a few years ago. These school's successes go in waves.
Of the 550 something public schools there are only 8-9 coaching staffs that can build elite programs? I don't want to get into an argument, but is it really that the other public schools aren't working hard enough as some have said? You could argue that those schools I mentioned above as elite have all the resources in the world, minus ESL. That I would agree with.
I'm not a private school hater by any means, I appreciate the tradition that goes with it. I loved seeing St. Laurence make it to state. That being said, I don't know if I buy that it's all on coaches to make their programs elite. There's a lot more to it than just outworking everyone. You need resources and above all, you need the players. If the players aren't always there it's tough to sustain being elite. Some schools have a wider net to find players.