While it's obviously the slant of this board, I personally don't think the IHSA should be doing anything based on how "fun it is for the fandom" - their duty is to all high school athletes. Remember that the kids getting blown out by Mt. Carmel in the state quarterfinals represent a tiny percentage of the players in this state - it's a very "niche" problem.
I feel like I'm beating a dead horse here... why are these DUDES going to private schools??? If you say "It's not coaching, it's not culture, it's DUDES", but then we can't point to any other reason why the DUDES are going there... It's probably coaching and culture. It doesn't mean that those coaches are wizards that can mold any bunch of random kids into a state champion, but it means that kids are attracted to the programs that choose to run themselves in the most professional and competitive of manners.
You have a fair point here, a winning tradition is a huge advantage. I would just posit that it's built on the back of what I mentioned above. But it's also not accurate to base an entire thesis on private schools around the two best teams in the state.
Loyola's facilities are meaningfully behind NT, GBS, GBN. You're right that Mt Carmel looks pretty good in comparison to the surrounding CPS schools.
Lol... you should tell this to DeLasalle, Pats, ND, Leo, Viator, Marian, Marmion, other Marian, ACC, St. Eds... should I keep going? They are missing out, some one should tell them they can play for state trophies!!
It isn't a counter argument! It is the ANSWER to the never-answered question of why these schools "get talent"! I sound like a broken record, but "it's not coaching, culture, tradition, etc., they just get talent" doesn't make sense if you can't explain WHY they get talent! Even your point I bolded above, that is a cultural element of the school. It's also a cultural element of say, Maine South, which contributed to their many dominant years. (a relatively outdated example but one I am familiar with).
I'm not saying this is "fair" per se - you may believe that public schools, based on their mission, are unable to build the winning ecosystem to encourage the best athletes in their district to play football at a youth level and desire to attend their school. The best ones have, for a time. It also doesn't mean that every public school has the inherent potential to win state championships if they did something a different way - they don't. Other factors are at play (some of which you referenced) that effect both publics and privates and will probably similarly prevent Westmont, Payton, and Christ the King from ever winning state, to use three very different examples.