I think most people would choose the tutor option because they wouldn’t want their children sent away anyway. And that's were it gets tricky. What teacher would want to sit in an isolation room with an angry, uncontrolled kid? How much would it pay and could it be sustainable? How many subject specialists would you have in any one establishment to accommodate the number of excluded kids there could be.. or how would you fill the timetable of an individual teacher to make it worth their while / cost effective?
Where would that be?
That's why PRUs exist. And they are a very mixed bag / can of worms.
Sorry, I know I am being negative, but the reason a solution as you describe does not exist is it cannot. There are no facilities, not teaching staff and no workable budget for it.
The only solution I can see is quite Draconian and starts not with the kids but with police action. A huge increase in police numbers and a will to prosecute and punish every single misdemeanour, from littering to BDSM/sex gone wrong murders.
Basically I believe that the perspective of a number of sci fi writers from the 50's - 70s is right: the health of a society can be guaged by one simple measure, every day politeness. Lose that and the society is lost. And, as that clip shows, we have lost every day politeness... in all ages.