Serverless email servers! Serverless DNS servers! Serverless web servers!
I believe you should see a problem there.
Serverless is a misnomer for this kind of thing; it's "-as-a-service" not long ago. Nobody manages their own email or DNS servers anymore. Webservers, maybe, but that too can be handled by a few hundred different services depending on what is needed.
> Nobody manages their own email or DNS servers anymore
Thankfully you are quite wrong there; lots of us keep running the services that were designed to be decentralized.
Agree, I call them and think of them as Lambda servers.