In the marine world a fresh water still is called an evaporator. Sea water is heated to apx. 165 F and boiled at 26" of vacuum. Usaually several stages. One third of the saltwater is ejected as brine. The energy cost is the phase change from liquid to gas, and for water that's pretty steep--and costly.
RO units use high pressure to force water through a special membrane (and waste brine too).
Ain't no free lunch.
The U.S. has a lot of fresh water--mostly in the Great Lakes. The states around 'em seem somewhat reluctant to ship it to L.A. though.