The problem is that a personal bank account doesn't qualify as a non-profit under U.S. tax laws. So donors can't write off the donation and the kid would be assessed income taxes on the donation.
Again, you're focused on a totally different issue. There's nothing wrong with splitting costs or reimbursing a friend who bought you something.
Splitting rent or cab fare, etc. is fine, but that certainly doesn't mean a H.S. kid can receive $50k in "donations" in his/her personal bank account without worrying about the tax implications. That's the issue the OP is trying to address.