If you're using replica set, as you should for anything other than development (and even in development, sometimes you need a replica set for some features), you just sequentially upgrade each one. It goes down, clients figure out the new topology and continue working.

I'm also running on MongoDB, top 6k site and while I wouldn't say there weren't any issues, uptime is wonderful, I sleep well, and have zero problems with modeling the domain as a document collections instead of relational. Can easily imagine that it would not be great fit for many other use cases. Not using Atlas as GP, so it's more work, but I'm trying to be scrappy.