However, my district also had a school specifically for troublemakers (with fences and extra security and all of that) so the other schools wouldn't have to deal with them.
Although for self-selected friends my personal saying is that "All the smartest left school at 15". My other friends are academically educted which doesn't smarten up anyone.
You seem to have a severe deficit of compassion. Also a deficit of strategic thinking.
Some significant fraction of those "delinquent kids" are that way due to some generational cycle of poor treatment and/or bad circumstances. If, as you advocate, little attempt is made to break those cycles, you'll just leave the problem to fester and get worse.
Also you're advocating punishing kids for being the victim of their own circumstances, which is just heartless.
The correct response to this situation is focus on finding better ways of helping those kids.
With who's resources and at the expense of what other things could be done with those resources. Money is fungible. A dollar spent warehousing problem kids is a dollar spent not helping the decent kids become good and the good kids become great. Education is a numbers game.
FYI, you're not a decent person, you're a problem person. You lack compassion.
If someone beats you and leaves you for dead in a ditch, when the paramedics find you, what should they say? It pretty obvious: "a dollar spent helping this guy could be used to help someone better, leave him for dead."