Do you have a recommendation for a major email provider as a fallback if you have to pick one?

I vaguely recall encountering a service that only accepted addresses from a whitelist of big providers (Gmail, Yahoo, Outlook, etc.), even @icloud did not qualify.

That's a service that doesn't want your business. If you care, message them about it

I've never once run into a service with such a restriction, but I can imagine someone being that short-sighted. I have seen services that only support "log in with Google or Facebook", which is comparably terrible.