Constructed wetlands have been used since the 1970's for swimming pools and look quite nice. They are ideal for northen temperature as well as tropical regions.
Who swims in the winter outside? Indoor can be done the same, but lighting is required then.
See Bionova, among others, the systems are rather simple and look nice, use less electric, typically use Ozone in place of Chlorine etc.
N and P are not really issues and mainteance is also a concern as well as looks. There's no algae scrubber in the world that will look nicer than flowering wetland plants. Folks see nice plants, clean water, that is inviting, mat of slime algae?
I do this at the lake level, we use sago pondweed and Najas. Water is nice and clear, we run some ozne at night. There are fish as well in this system but it's certainly nice to swim in(A tad cold at 65F in the summer).
Once you get into FW, the wetland emergent plants cannot be beaten for nutrient removal rates and ability to sequester nutrients/Xenobiotics/waste etc.
You also have their sediments which also cycle these waste.
See Reddy and Debusk for more on the topic at the waterwater level and the smaller applied level, as well as googling constructed wetlands, filration and swimming pools.
Ok I'll try to check into those. I guess my focus here is the average residential pool, where the users can't/don't want to use chlorine. Something need to control bacteria, and something needs to control nuisance algae.