Depends on what you want. If you want uptime, then sure. If you want to be able to blame someone then no.
If you are down for 1 hour a year on self hosting, but Office 364 is down 3 days a year, your CEO is going to be more understanding of the Office outage as all his golf buddies have the same problem, and he reads about it in the NYT.
But in any case zero downtime is difficult, that's why you need two independent systems. I had a a 500 microsecond outage at the weekend when a circuit failed which caused an business affecting incident, not a big one fortunately, as it was only some singers, but it was still one that was unacceptable -- had it happened at a couple of other events in the last 12 months it would have been far more problematic. Work has started to ensure it doesn't happen next year.
this, ladies and gentlemen, is why you should always self host critical infrastructure