(Your second number is off -- it's 2,260 kJ/kg or 2,260,000 J/kg)
There's no therodynamic objection that you can't recover (virtually) all the heat you spent creating steam, when the steam is recondensed back to water. Which is what they do. Distillation methods (multi-stage flash (MSF), multiple effect (MED)) "only" use around 200-400 kJ/kg of heat per water output.
Some perspective: at $4/thousand cubic feet natural gas (US of course), this is a heating cost of $0.75-$1.50/cubic meter of desalinated water. High, but not impossible.
Pretty much anything you can do is cheaper than boiling water