Nice analysis. But the premise of the discussion here is that people do the desalination for its own sake, not in order to harvest Uranium.

This [1] article from 2012. It presents a Uranium extraction method from seawater that would put the extraction cost at $300/kg. Nowadays the market price is about $70/kg. However, if method were to be applied to brine instead of regular seawater, maybe the cost would go down. Hard to see it going down by a factor of 5 though.

[1] http://large.stanford.edu/courses/2012/ph241/ferguson2/