I almost replied to your terse OC to disagree [1], but I think this explanation is extremely insightful and worthy of attention and upvotes[2].
I call it the myth of the commodity server, and it's particularly prevalent among software engineers, since the natural inclination is to approach every problem as though it can be solved in software. Perhaps ironically, this often excludes the kind of software sysadmins write, which is deployment and configuration.
Far more importantly (from my POV), such an approach ignores the importance to cheap, reliable scaling of being able to customize the arrangement of the hardware [3].
Pretend that all servers are the lowest common denominator, and scaling gets expensive fast. Often the end result is more/earlier customization of software (e.g. writing a distributed DBMS from scratch, which takes on a life of its own, not getting any cheaper), and I can't imagine that's cheaper than hiring a sysadmin to customize configuration and deployment cheap hardware (which does get cheaper) to get mind-blowing I/O.
[1] I still do, in the sense that I feel it implies that the server hardware or its operation is anywhere near as expensive as employees. I'd be quite surprised if any startup spends more than one tenth on servers as it does on people. However, your point that some people are required when one has enough serious traffic is one with which I do agree and one that is often missed.
[2] Bias disclosure: I'm a sysadmin
[3] Which effective customization requires knowledge of and experience with