As opposed to, say, trad folk.

I think if you opened your ears you'd hear a lot of living Traditional Folk musics in which improvisation plays a signifant role; probably less so in the UK revival which is hardly a living culture.

It's how the term "classical" is being (ab)used.

I suggest you read the previous posts from myself & Spleen and maybe do a little rooting around on line with respect of the classical musics of different cultures.