Main thing with swimming pools is that kinds chosen not drop small parts that get sucked into filters. Otherwise all trees give off old bark pieces, leaves etc. With the first order of business being what your geographical location is.

It's probably better to get a good cover than to worry about the trees. Save water, save chemicals, reduce maintenance, and grow what you want.

Fern pine - Podocarpus gracilior - is a very poplar plant used for this purpose in CA. It will need some pruning to keep to a narrow profile. Clumping bamboo species are another possibility.

And I'd also agree about investing in a retractable pool cover to keep necessary cleaning to a minimum.

I find a lot of my bamboo ends up in the pool, and I don't even have that much. But is it so horrible if leaves get in the pool?

I suppose something like giant bird of paradise might work if you really don't want stuff falling.

We had clumping bamboo (Bambusa Oldhamii) in CA. It worked great to quickly grow and screen a 2 story house that was built just up the hill from our house. Unfortunately our other neighbor's pool was on the other side of the wall and the bamboo dropped lots of leaves. We had no problem with them pruning anything over the wall, but stuff still got blown on their side. If the bamboo won't be right next to the pool, then it is worth considering as a fast growing screen. That is also assuming you live in a climate that will allow you to grow this variety.