I wouldn't really consider much of today's music (esp. popular music) as art. Paying to support Michelangelo is one thing, paying to support Eminem is something entirely different.
Wouldn't the same argument apply to movies? So it would then be the taxpayers paying Tom Cruise $50 million for another bad movie?
This is, indeed, the heart of the matter. Public funding of the arts has to offer
a. Wide and lasting
b. Excellent value for money.
Of course, these two factors are related. It costs a lot of money to produce the tawdry studio-engineered pap that passed for music these days (sorry, can't help being old), and in a year's time it's forgotten without regret. OK, so there are exceptions, but not many.
It costs a lot of money to put on and record a full performance of Handel's Messiah
-- a heck of a lot of money. But since people have been listening to it for getting on for 400 years, it's a fair bet that it will continue to be in demand. Of course, the same could be said (on a shorter timescale, of course) of the Beatles, or Pink Floyd, or any number of others. But it's difficult to predict at the time
what's going to last and what's going to sink without trace.
Public funding of museums and art galleries can offer good value for money, because the number of people who benefit from them is pretty large compared to the amount the cost to run, especially when averaged out over decades. I just don't see how that's going to be true of modern music, which is almost always ephemeral.
(Of course, most music of the classical era was ephemeral, too. But we at least get the benefit of hindsight with that, and a very long period of Darwinian selection to weed out the rubbish).