So for clarification.
I see the division between different types of music being defined, and made valid, by each of the different types of *listening* required for each.
And, regardless of basic style, I see the division of 'popular' and 'classical' as a division of listening intents and types.
I'm a big fan of 'progressive rock', and I hold this in similar regard and respect as modern 'classical music'.
Away from the extramusical factor of compositional method (and in the case of prog - often recorded improvisations which become composition), the differences are - by and large - just timbral aesthetic, focus on 'beat'(and percussion as driving force), and less rhythmic freedom(dynamic too in many cases).
You have one thing, and you forego another - you have a steady loud beat and you lose overall dynamic subtlety as well as the whole world of 'rubato', but of course - it doesn't matter because they gain as much as they lose, with their priorities.
Back to the point - these elements can surely make up a 'classical piece' if only it were termed as such....as it still falls under the same broad kind of listening 'classical' requires.