You have brought a a bunch of very interesting questions here--and important ones too, because though the situation appears to be very different here in the states, in terms of both classical music and radio--the effects seem oddly similar--radio programming seems to offer a very narrow range of choices, and there seems to be an extreme polarization between classical music and all the other stuff--
A lot of the American music schools now offer jazz programs, and a fair number of the high profile pop musicians have had extensive training in classical music, though they do not tend to admit it-- heavy metal guitarist Steve Vai,is I believe, a Julliard graduate--and there are many others--
Years ago, when classical music was regularly featured on the radio and television, and many (if not most) of the classical conductors, composers, and performers, were European exiles, there was much more enthusiasm among them for folk and pop idioms--and it was typical for performers to include folksongs and arrangements of folk music in their performing repertoire--
For that matter, the pop and commercial jazz musicians, at least until the fifties or early sixties, generally read music and worked from arrangements--and were on playing terms with most kinds of music--(pop and jazz renditions of classical tunes used to be quite common)
For quite a long time, though, the different branches of music have seemed to be at war with each other, with people who stradle the fences of taste viewed as traitors of a rather high order--
I have no idea how we got this way, especially since it often said(way too often) that music is a "universal language"--