Well, the headache is in making careful selection and configuration choices.

Done properly, it really requires very little ongoing maintenance. Maybe a few hours per year. DNS requires even less.

Spam filtering? Security updates?

Depends on your experience level. If you have never setup postfix/exim/sendmail to do more than accept local mail then it will indeed be a giant headache. With a bit of work with dovecot and postfix you can have yourself a very nice mail-server. That said, there is a point at which the self-hosting pain point is not necessarily realistic, and if you have two accounts you need and they're $4/month elsewhere, why bother would be the discussion to have.

Generally you don't want to host email or DNS yourself but I think if done right and you keep them on their own servers it can be great in the long run.

I am a fan of self-hosting, right up until the point it crashes on you and you have to spend a weekend fixing it. You are right, email is one of the biggest headaches out there.