I'm well aware of that.

Unfortunately, its well-established-ness is only useful when talking with people who are well informed on this stuff, which most people aren't. See, e.g., the fact that Luke (who is generally well informed about things, and interested enough in this particular topic to be writing evangelistic webpages about contemporary art music) is choosing to use the term "classical" and proposing "new music" as an alternative.

So: yes, you can say "art music" when you mean art music. In that case, your usage will be correct and you'll be accurately understood by music experts; but to anyone at roughly Luke's level of expertise and below your meaning will not be clear.

Or you can say "classical music" and make, where necessary, appropriate disclaiming noises. In that case, your usage will be incorrect and some music experts will look down their noses at you a bit; but people at roughly Luke's level of expertise and below will have a reasonably idea of what you mean.

I generally choose the second option unless I know I'm addressing only experts. I wish there were an option that combines correctness, broad comprehensibility, and conciseness -- but I don't know of one.