The high school I attended now limits college applications to 10 per student so that “schools will know that the student is serious.” Can’t say that I love their approach, but I can imagine that some private schools might do this for BS, less to show seriousness but to keep their students from cannibalizing each other – especially given that the BS universe is small and most of the schools are also small.
With that said, I don’t know of any schools that do this.