If my custom media server or private photo site setup fails, it is not a big deal. But if I can’t login to a shopping site or my family can’t checkin to a flight because the two-factor auth email disappeared in to thin air, I am the “horrible IT person” who spoiled Christmas - end of story.
You can script checking those, but you'll have to re-implement it for each provider. And there are some that you can't; if I'm applying for a job, they're not going to give me an email account to test whether my stuff is deliverable.
HTTP services are absurdly easy to monitor in comparison.
A mailserver administrator is a sysadmin. Being a sysadmin is on the face of it unrewarding - nobody pats you on the back when everything is working normally. They only call you when there's a problem (and it's usually urgent, and sometimes critical, and they'd like to know who to blame). So if you run a mailserver with users, it starts to become a people job, and things begin to matter.
People certainly rely on email to a greater extent than other services - even mobile. I can order goods online without surrendering my mobile number, but I always have to provide an email address before I can complete the order.
But I've still enjoyed administering mailservers. Perhaps I liked the slight paranoia induced by trying to reconcile the boss's demands for functionality with his demands for security.
Yes, if you choose to run a service it will need to be maintained, and occasional issues will come up.