I know this used to be the case, and makes a certain amount of sense when each box is physically accessible, but it seems unsustainable in the Cloud Age. Perhaps each online service we provide can be whimsically named, but that seems impractical for the constellation of DB servers, caches, app servers, load balancers, etc. that support a typical service.

I'm not sure about that. If management won't let you name the servers after characters in your favorite sci-fi movie, then that is an indication that names matter (ns1 for DNS rather than gandolf or papa_smurf or whatever) and that management is playing the role of the adult while you are acting like a child.

If you want to name servers after fairy tale characters and you will have a tantrum if management won't let you, then you are not mature enough to work for a company. It's called growing-up and being responsible.