At best, I think the NEA fills gaps that just ain't there.
I've done some work for a theater company in the past (which shall remain nameless lest my screed embarrass 'em). They do incredible work. Incredible fucking work. They pay their performers and staff decently. And going to one of their shows is at dinner-and-a-movie prices.
The reason they can do this is because of multiple revenue streams. One is corporate and high-roller donors (who get season tickets and their names in the programs and whatnot). Two is the box office. Three is grants from the NEA and other organizations.
Because of those grants, college pukes can take their dates someplace classy. Old folks on fixed incomes can go somewhere nice on special occasions. And the company can go on the road to the far corners on the state, where high school kids who have never set foot in a theater can take a break from reading one act a day in a boring English lit class and see some Shakespeare as intended: live, in front of their eyes, done by shit-hot pros.
Now, if those grants went away, would that company go away? Maybe, maybe not, I don't read their books. But at a guess, I'd say they'd probably have to cancel their outreach programs, do fewer shows a year, and their ticket prices go from "dinner and a movie" towards the "rock concert" range. Probably wouldn't shut them down. But it would turn them into something cool you could only see if you were rich.
Does the NEA also fund stupid shit? Undoubtedly. In a world of "may the best grant writers win," that's probably inevitable. But say it is ten cents of my tax money a year. Last time I went to a movie that sucked, it cost me twenty bucks. That means the price of a shitty movie gets me 200 years of cool stuff like the company I just mentioned. And Sesame Street and Nova and probably a lot of other programs I haven't heard of that have done cool stuff. If it funds a lot of crap in the process, so be it. That's not a problem of funding, it's a problem of people being shitty artists but good grant writers, and NEA personnel not catching that.
We are nowhere close to the bullshit level of say, France, with warehouses full of publicly funded art nobody wants to buy and CD's full of publicly funded music nobody wants to listen to.
We're still getting some bang for our buck.