I like the idea of an elevated pool cover that uses different tricks to catch heat.

Since most heat is lost through evaporation, and the cover itself reduces that, what is needed is to use both passive and active means to heat the water.

In the fall and spring, when humidity is lower, but there is still a lot of sunlight, solar cells could power a slow pump, that would draw water up to just above pool level, then slowly flow it through winding blackened pipes to heat. It would then flow into the pool pipe system, and be returned at the bottom of the pool, not the top.

In winter, the solar cells would heat the water directly. While much less efficient, it means that the water will need much less heat to be acceptable for swimming again in the spring.

And in summer, the cover would have to be removable.