Self-hosting inbound email is trivial. Anybody will send email to any random domain, they're just not willing to accept it from random sources.
And the latter is what is relevant for password recovery.
I self-host inbound but use established servers for outbound through my ISP and have had no trouble with that setup for a while. Forwarding to people through my domain has gotten a bit more challenging lately but I've got it working well enough to satisfy gmail so far. (The advantage with forwarding is you only have to convince one server to accept it, not everyone in the world, and there's some crypto stuff involved now that involves trusting some keys, not just a domain or IP, which also helps a lot.)
That is simply not true. I have self-hosted email service and starting about 1.5 yr ago some big email services don't deliver emails to my server anymore. And there are many similar cases reported...
So one can say that even if an independent email service is willing to accept email traffic from any sender it does not guarantee that customers of all other services can have delivered their emails to addresses at the service.
In terms of authentication, this is not entirely true. It's less common these days, but I used to have a lot of trouble with sites rejecting my attempts to create accounts with e-mail addresses from my disposable-e-mail-generator of choice.
Not sure what kind of crap some folks are smoking, really.
Well, I suspect those are more specifically blacklisted.