I mean, depends on use case right? Certainly for travel and navigation purposes I very much want to know when I'm about to leave a country :-). For any economical or political review as well, country birders are extremely relevant data.
There certainly are geology and other scientific endeavours which perhaps don't care too much for countries, but even they probably need them when they interface with regular humans (I.e. This lake is in such and such country, this volcano is about to explode over there, etc)
Tourist endeavors really care about borders for 2 aspects: as barriers, and as places where legal or social rules change. If administrative borders had their powers limited to, say, statistical purposes, and not social obstacles, a tourist would stop caring about them.
Interfacing with humans does not necessarily have to be done along social borders. I'm sure it wasn't that way before the rise of the nation-state. Everyone knows where the Alps are, or where the Great Lakes are. Pretty much every place on Earth is covered by some geographical-not-political area name. Why shouldn't places be referred to in that way? It's harder to politically push for a change in the definition of the Gobi Desert than of an arbitrary administrative unit.
If I'm reading it correctly then, you're aftually advocating for a massive paradigm change in our social and political life, and not for a small UI change in mapping software.
Which I did not pick up from your initial post within this context, but fair enough!:)
I'm actually curious about the UI change in mapping software as well. The current cartography is focused on human-scale things, rather than geological-scale things. It's hard to find a map that gives topography as much space as it gives to roads, even when visiting some mountain ranges. In the lowlands, tourist maps still focus on roads and town names disproportionately more than on the type of environment and natural landmarks.
On a global scale, when the country borders are removed, we find ourselves lost, despite the huge ecological and geological diversity of the place, which makes our - or at least mine - experience as a inhabitant of this amazing place so much poorer. Compare the difficulty of finding the Atacama desert versus Luxembourg. How often do you see a whole-Earth map with the desert marked but not the state?
There certainly are geology and other scientific endeavours which perhaps don't care too much for countries, but even they probably need them when they interface with regular humans (I.e. This lake is in such and such country, this volcano is about to explode over there, etc)