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.
replyYes you can.
replyUser 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.
Deeply unserious take.
replyAs unserious as you claim, we had this exact problem.
replyEmails would be accepted by Outlook.com, but would never deliver. We had SPF/DKIM/DMARC and full reporting. They RBL'ed us with no remedy.
We told the customer to not use outlook.com BECAUSE we told them we could not guarantee any delivery of messages.