Because the college kids want to play, and because everybody wants to get paid.
The college football season can be argued both ways. Those who thought it should happen point to the games that were played. Those that did not think it should happen point to the games that were postponed.
College basketball will be the same. It's going to try to avoid the chaos as best as possible, and keep things as normal as possible while being as safe as possible.
It's the same as every other business out there -- trying to get by.
And yes, of course it is a business.
(One more thing: The debate that is coming is an interesting one. If most colleges are having kids stay at home for online learning second semester, it probably decreases the risk of virus-related problems for college basketball teams. The question will be asked, and it's a fair one: Should student athletes be on campus practicing and playing when their peers aren't on campus learning? It's a fascinating debate, but the answer is they will be, because of the first line of this answer.)