There's quite a bit truth about your comment but I think it is somewhat simplistic. To better analyze your objection, let us remove the taxpayer part first: Should art projects be funded (by whatever means) that the general public sees no value in, i.e. this is how I parsed your "no one would pay for". This goes into deep discussions about "what is art", "how do you define the value of an art object" etc. Without going into detail, let us observe that in almost all art fields it frequently happens that even the educated public's taste lags the appreciation. I don't know much about painting/sculpture etc. but examples abound in literature (one of the most famous is
The Great Gatsby) and film.
So, the mechanism here is very much similar to entrepreneurship: an artist producing work of dubious value asks for support, there's considerable risk in this, i.e. the work is most probably is junk but you might as well have discovered the new Warhol or Banksy. Therefore, it's not a case of funding works "no one would pay for" but how to manage the risk.
The bigger question is: should the state be in this business, with its clueless, bloated and generally ineffective machinery? Again, avoiding the long discussions about how controlling government should be I propose (the obvious but somewhat naive) solution: government should fund some reasonable amount but the works so funded should be under joint ownership of the artist and the public, i.e. the artist should own it but the public should have perpetual view rights, at least from a web site. Continuing the NEA example I gave above, the text of those translations should be available from the NEA site. The public should get value in return, other than the moral feelgood effect of supporting artists.