> If in any given phrase one means Ukraine as a region, like Caucasus, then it is "на", if one means Ukraine as country then it is "в".

There is no such semantic distinction between these two prepositions.

You speak of a human language as if it were a programming language disregarding its history (while even for programming languages, history is important, which is why javascript or php are in the state they are currently in). Just as no-one was thinking of the troubled American past when they were using the word "master" as a name of their default git branch or of the primary database, so no Russian (at least none that I am aware of) relies on the preposition "на" to tell them that something is or is not a country. They do, however, rely on their vocabulary of linguistic collocations, developed through the years of using the language, that tells them that the word "Ukraine" wants the preposition "на".