I went to a few lectures on mathematical music theory once. I've forgotten most of it, but I recall learning that most of the music I can enjoy (pre-1900 Western classical, 20th century pop and rock) is, structurally, confined to a very special case among all the possible scales that a music system could be built on. Someone like Schoenberg is to all the other music I listen to, as Mars is to all the different continents of the earth.

This view is mistaken. It's not, mind you, your mistake, but that of the music theory community, which has egregiously, utterly, and persistently failed to carve musical reality at its joints. In point of fact, Schoenberg uses the same set of pitches that the composers you like do -- the ones you find on a piano keyboard. And contrary to implicit music-theoretical tradition, you don't have to pretend that those 12 pitches in the octave aren't the same notes you're used to, either.

In simple terms, the difference between Schoenberg and the music you like, and the reason people have trouble with the former, isn't that Schoenberg isn't in any key, but rather that Schoenberg changes keys so quickly and constantly that your ear has trouble keeping up and feels "confused". A note may literally be "in a different key" from the previous note. There is much less redundancy to reinforce the "meaning" (i.e. position within a diatonic scale) of a note; you have to "catch" it immediately.

You can see how this state of affairs would have been the product of gradual evolution, something analogous to an inferential chain -- with more information content being packed into music with each generation of composers.

The point is, it's a quantitative difference, not a qualitative one.