Cost vs efficiency doesn't really become a factor until further increases in efficiency are very small with the cost of those increases very high. This (to me) is all about extracting as much heat as possible. The cost is spent only once. The energy extraction is forever.
Hose on the roof is definitely good, though. Anytime I drain and refill the pool, I run the water through several hundred feet of black hose run around the pool and a lot of heat gets gained that way. In fact, this whole project started with pumping pool water through a bunch of black hose.
In my particular situation, there isn't a sun-facing large roof anywhere near close enough to the pool to make it worthwhile to drag the hose up to the roof.
Edit: If I took my son's variation and made it very large panels covering the roof, I bet the water flow would need to be really high. Even with my comparatively inefficient prototype, if it were roof-sized, the output might very well be steam at the volumes I was dealing with. It would at least be extremely hot.
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