Excelling at D1 football or men's basketball requires an incredibly strong commitment of time and money. If you're going to do it in both, you're taxing your resources even more. Not many private schools can afford to do both, let alone decide to do both.
You listed SC and Miami in your post. SC basketball is terrible and has been so for as long as I can remember. With one or two exceptions, so has Miami basketball. No one you put on your football list has done both consistently well.