>But surely the managers of people who maintain those servers are part of the cost of maintaining those servers.
you were raising an irrelevant point, because the salaries of the direct managers of the operations team is not what's under discussion here. They wouldn't need such a deep organizational structure if they weren't paying a bunch of people that take no part in running the site.
Even if you cut everyone doing software development (which would in itself probably cause a collapse since that is critical to keeping wikipedia running), cut all the lawyers (also pretty important), cut the trust and safety people, etc - you are still left with quite a lot of sysadmins, more than can reasonably be handled by a single manager.
Now, if your primary objective is not to run a website but something else entirely, then it does make sense for your infrastructure and the salaries of the people maintaining it not to be the largest part of your budget.