Billing exists for servers as well.
Servers need to be configured as do lambdas.
Servers also have backup needs.
Servers also present security problems of access.
It's not that hard to configure a lambda to run in just as limited a way as a physical machine.
Not having to worry about MCEs or disk failure patching makes the concerns less like a "different set" and more like a subset of things to worry about relative to managing servers.
I know most of this stuff is really well trod-over, but from your comment I think one'd get the impression that people are switching just because of a trend or something, not because there's an actual layer of management they're paying to have outsourced.
(I would acknowledge that view of it being a subset rather than a different set is invalid once you're debugging performance at a gritty level, where cold starts etc. etc. introduce their own equivalent layer of complication, but most people doing most things never need to)