There isn't much breaking usually, I really don't remember big issues in my 15+ years self-hosting time. I have changed colocation place several times, some places have been offices with average office internet (without redundant links or BGP peering).
I can see issues, if you over-engineer and try build some microservice farm in some cloud provider, but simple physical server with DC grade disks in RAID and backup (tested and out of server) is pretty reliable.
Of course, when you really don't want to do it, then paying for someone else is reasonable, no issue with that. But its not fair to make mail self-hosting look like something very complicated and dangerous, I would say that modern web service stacks are more complicated and fragile. Lots of guys here are writing own internet facing software, handling customer data. Compared to that, using pre-existing mail server software isn't that hard.