Shambles, I am a classical musician as well as a practitioner of other forms. Here in the USA we don't have State radio per se, although we do have "public" radio stations that survive on private and corporate donations supplemented by some government funding. They tend to be more eclectic than what you're describing, devoting substantial amounts of air time to folk and acoustic musics, musics from other cultures (commonly called "world music," although some of us don't care for that term), and a variety of other things.
However, even though there seems to be more variety on American radio, there is still some snobbishness associated with classical music (we don't often use the word "proper" here). I think that snobbishness is a big part of the reason that people aren't drawn to classical music nearly as much as they are drawn to pop music. Basically, the classical world dug its own grave -- the classical institutions did their best to choke all the life out of the music that people often don't want anything to do with it. Improvising and creative license are frowned upon (except within very narrow parameters). The young prospective music student is basically encouraged to believe that the best he or she can hope for is to work like a slave for decades to play this music almost exactly like everyone else does -- and if he or she is VERY talented and EXTREMELY diligent, ready to sacrifice everything to the quest for technical proficiency, perhaps there will be a seat open on some orchestra somewhere when the last occupant dies. Is it any wonder few are drawn to this?