On the management side, I'm curious what you mean by "most of the server are not managed by you anyway". In my experience, unless you're in a very big company, you are either managing or at least minding the server, or someone within earshot range is.

In that scenario, not having to even consider if the error you're getting is because your server is restarting/out-of-memory/needing-update/broken-by-a-coworker like 99% of the time is as close to "serverless" as it gets, in terms of day-to-day work activities and worries.