unless the account isn't important - don't. By the time you have a setup that isn't at the mercy of ISP outages, blackouts, misconfigurations etc. you have invested a load of time and money for not much gain.

Which makes me wonder: how hard would It be to offer an email service as a self-hosted app?

So you install this on a home always-on RaspberryPI or something and, after filling out some details, it just works. Would that be possible at all?

Some scripts that in the background get the right certificates and set the right records and so on should be possible, no?

From what I gather, yes, that would work, but no, it wouldn't. Apparently all non FAANG mailservers are one misstep away from being put on all blocklists in perpetuity with minimal chances of appeal.

There's so much babysitting required.

I've managed to wean all but one of my clients off self-hosted email. They are paranoid and insist on keeping it in-house. It's such a big time suck to deal with spam filter tuning and blacklist removal requests and the like, but they keep paying the hourly rates for it.