I would argue, that you inadvertently learn the names once you learn of the context. I would see it more as a filing system. If there is nothing it points to, whats the benefit of knowing it in the first place.

This is just a syllogism. Context -> names. !names -> !context.

So we can tell that a guy who hasn't heard of eigenvectors (name) doesn't know much about linear algebra (context).

I think the analogy lacks. You can know quite a bit of for example the Kurdish conflict in Turkey without knowing the names of the Turkish sates in question. The province centric approach is one of the major problems that foreign powers faced in for example Afghanistan or Iraq, where the cultural spheres dont align with province borders. As a worst case, what good does it do if you know the name of the province but brought a translator speaking the wrong language.

A similar argument could maybe be made for voting preferences /political leanings of the different regions in the US to give a more practical example.

But yes that is rebutting my last comment. You dont necessarily learn the state names by learning the context.

I don’t need to know the names of Chinease subdivisions to know most people live on the eastern side, the west is dry to the north and mountains to the south etc.

Knowing similar things about the US tells you the area Texas covers is dryer than average even if you don’t know the name Texas.