That may be so, but you can't control what mail service your recipients use. So whether or not it's a bad idea, it can be your problem. That said I don't agree with OP that self-hosting mail is a bad idea.
Yes you can.
User signs up, uses @outlook. Your app declines it and explains that they block with no way to remedy, and explain they are a bad vendor.
Yes you can.
User signs up, uses @outlook. Your app declines it and explains that they block with no way to remedy, and explain they are a bad vendor.