High school? Yeah, it would, but not for reasons you think.
You say that as if totally unaware of the existence of postseason tournaments in the other classifications of college football. Almost as if you completely ignored everything I said other than the letters "HS"
FCS: 127 teams, 10 games against 10 opponents, 24-team playoff (maximum of 15 games)
DII: 169 teams, 10 games against 10 opponents, 28-team playoff (maximum of 15 games)
DIII: 246 teams, 10 games against 10 opponents, 32-team playoff (maximum of 15 games)
FBS? 130 teams, 12 games against 12 opponents, and we'll not mention the playoff size because we haven't even established to which one you're referring.
Oh right, but you brought up HS. Ok. Well I didn't look at the precise numbers in other states, but I'll just tell you how it works in one division in Texas (since they're all essentially the same):
5A Division 1: 129 teams, 10 games against 10 opponents, 64-team playoff (maximum of 16 games)
It is dishonest to assert baseless speculation as though it were a matter of fact. There are 3 different NCAA tournaments in the sport of football, 2 of which concern leagues of noticeably larger size with shorter schedules. Tell me about all this trouble they've been having with achieving with "orderly post-season tournaments."
I can't even believe I'm entertaining this because the notion is so stupid, but yeah they have, and the answer is the same: it'd be a logistical nightmare. The easiest way to even conceive of doing it is to construct a 50-team bracket of all 50 of the state champions in the top classifications of each state. Here are the problems with that:
1. There's no central governing body for high school football in the US.
2. You're, therefore, going to have to deal with 50 different governing bodies, and their rules aren't all the same, either. So whose rules are we playing by?
3. A 50-team bracket means 32 teams would get a bye. How do you go about sorting that shit out?
4. In addition to the 16 games that a lot of states require of their state champions, you're going to have to dedicate 6 more weeks of that. So that means that to play in the National Final, you'd have to play 21-22 games. Not even the NFL requires 22, and to get to 21 means that you'd have to be a wildcard team.
You're comparing a seemingly impossible concept like a national high school tournament to a league that is as large as, or smaller than, its most immediate counterparts at the same level. That's about as dishonest as it gets.
Oh and just FYI, no one serious gives two shits about that stupid, mythical "national championship" at the HS level. It's an absurd concept that includes an indefinite number of teams (there are between 4 or 5 every year), there's no governing body or any entity that even rewards a fucking trophy. It's just mumbo jumbo that websites and sports networks vote on every year. Meanwhile, the players and coaches can hardly be bothered to even care. They care about the state title, yes, but national? Shit, I even knew a guy who played for the 2004 SLC team in college that won it from 4 different services that year, and he wasn't even aware of it for like a month after they "won" them. The fucking guy graduated in the spring of 2006, which meant that he was at the school for 3 state championships they won in those 4 years and I never heard him say anything like "yeah man those 3 titles were really special but the 2004 one meant the most because some websites said we were national champions!"