By the same argument, replacing the coal fired power plant with wind and solar wouldn't pose a challenge either.
The point is, you've got to compare apples to apples: either coal power vs. desalinization powered by coal, or renewables vs. desalinization powered by renewables. In every case, the pollution produced by the desalinization process (i.e., the brine etc.) is simply added to the pollution produced by whatever means was used to generate the power for it, which means @soEZ's attempt to compare desalinization to power generation doesn't make much sense.
Housing shortages are caused by bad government policy: namely, low-density zoning. Direct your anger towards the entity that deserves it, and make them fix their fuck-up.
(Note: I'm not making some kind of Libertarian "all government is bad" argument here. I'm saying that in this specific case, the laws need to be changed.)