Also, this is absolutely NOT a customer issue. It's a restaurant issue to clarify. Plain means different things at different restaurants, so the solution is to _always_ clarify exactly what the customer means.
I have this conversation enough that I now call out "plain no cheese" and ensure "no cheese" is written on the ticket.
Also "I'll take a number 3 meal plain" is void of an actual subject for the type of burger.
That's a fun regional difference with McDonalds it seems, we definitely have (literally) "Cheeseburger" as a independent item on the menu compared to "Hamburger" here in Spain: https://i.imgur.com/XDNuiUW.png
That's quite funny actually, Spain tends to translate everything and have everything in English, dubbed, but apparently the McDonalds Cheeseburger got to remain, and wasn't renamed to "Hamburguesa con Queso" as one would have expected :)
For a "cheeseburger" cheese is obviously integral. For a Big Mac, it's less clear but a "plain" Big Mac usually includes cheese.
For a fancy place's "deluxe Wagyu beef burger" that has cheese/truffles/a bunch of other stuff, a "plain" version will likely not have cheese.
Further, they _only_ showcase the "burger with cheese variant" in their combos and special. This further drives home that you should be thinking about cheese in the same way as toppings.
But one thing I know for sure, in Germany they are called Cheeseburger, not only called, but written as such on the menu.
Isn't it up to the person who is receiving the order to ask clarifying questions then? Since they know it's potentially unclear/ambiguous, why not try to resolve the ambiguity before making the order?
If you're clarifying at this level, there are likely many other questions that you'd ask.
Whenever I took my kids there I told them "if you don't want it the way they make it then don't order it."
Hard to know for a fact without knowing where I live, I'm guessing :) FWIW, it's not true at McDonalds in Spain, they definitely have popular stuff sitting behind the counter for longer than the items you customize here.