There absolutely is.
All you need is a bunch of mirrors to direct the sun at a chamber filled with water. The water will evaporate, the expansion into steam creates significant pressure so you can run it through a turbine, and then once the steam cools down and liquifies again, it won't have any salt in it.
It's not even remotely expensive. Mirrors are cheap. The turbines/etc are basically the same as a coal or gas power plant and mirrors are a hell of a lot cheaper than mining coal or gas. Also if you're boiling a usable quantity of water you'll be generating a lot of power, which is a handy byproduct (more valuable than the water to be honest).
"Not in our back yard" is the real issue. The chamber is generally at the top of a tower, and even painted black all that sunlight focused onto it is very bright. People generally don't want a really bright object on top of a tower anywhere near them. I guess you could build a wall around it or something, but you'll still get complaints from aircraft/etc.
Driving into the sunset or sunrise is annoying. Imagine if that was all day every day instead of just for 20 minutes or so.
Having said that, if you're in a remote area to counter the NIMBY issue, and clean water is hard to find, then the system I've described is very effective and they are being used for cost competitive farming of cheap crops.
Anyone who actually wants to desalinate seawater can do it. It's just that almost nobody wants to right now.