It does happen already - usually when teenagers have some stable family around who can have them for Xmas, summer, Easter but would struggle all year.
But I strongly doubt any boarding schools would want to take many of the teenagers in foster care who are - because of repeated failing by their parents and lack of financial heft from social services - quite fucked up, angry and difficult.
Not sure Jemima and Tarquin's parents, who are paying 40k a year, will want the likes of them in the same school as their kid.
Plus what happens in the holidays.
It's one of these policies all politicians like to trot out on occasion but which is much less likely to be helpful than actually funding social workers and foster care adequately.