If by strawman, you mean fundamental laws of physics, then yes, you’re correct. If we find ways to break basic laws of thermodynamics, then I won’t be worrying about ways to sterilize water, I’ll be worrying about how to make faster-than-light starship.

The part you’re studiously ignoring is plenty of people saying yes, you could do this, but that it’s wildly inefficient. You could also power a bike by getting the biggest rock you could throw, tying a rope to it, applying the brakes on your bike, throwing the rock, releasing the brakes, and then pulling on the rope until you’ve collected your rock, and repeating until you’ve reached your destination. This will always work. But as long as your bike is in earthlike conditions, there will always be easier ways to do it. This is also the case for your idea.

This is simple math. We would need to increase our energy production by 1000 times to just treat water, maybe only 250 times if we used more efficient systems than simply heating it and letting the heat dissipate. If we doubled our energy production every year, it would still take a decade to do it (8 years if we were aiming at 250 times). That isn’t a realistic amount for a civilization at our tech level.

What exactly do you think evaporation ponds are doing, then?