Well of course not, because schools don't have the support they need to help those students in turn.
>>goes to work at macdonalds
I don't know where you live where employing 15 year olds is legal, but even if we assume some kind of state where it's allowed, what mcdolands would employ a 15 year old that was expelled from school?
>>and comes back later,
How would that even work? You mean they enroll back at a private school to get their education? With what money?
The path isn't "well they get expelled so they just go to work" - most likely the path is that they just stay at home doing nothing all day if their parents let them, or they just turn to vagrancy/crime. No 15 year old is going to go "well I got kicked out of school so I better look for the most basic job" - it's some kind of unrealistic pipe dream of how society works.
But either way - you haven't really answered my question. In most places a child has to be in education until they turn 18. So when you kicked them out of school at 15, what is the state supposed to do with them?