Being an aerospace engineer I went through those calculations for my 33,000 gal pool. Talked to some guys at the pool supply stores and they all told me to do the solar cover. I put it in place and in about three days the pool was perfect temperature. I then learned to remove the cover on a regular basis depending on the season or the pool would heat up too much and destroy my chlorine content. The cover allowed me to use the pool from March to November without using my gas heater. I used the heater for the jacuzzi of course.
An engineer friend built his own radiator and valve system for his pool because he didn’t want to spend the few minutes it took to remove a cover. He spent a lot more money than I did but we achieved the same result.