I've thought of trying to build one, but it's several projects down the fantasy highway, still. There two directions to go to avoid chlorine (or bromine) irritation.
One is alternate chemistries, like various salt-water schemes, metal ionization, or UV irradiation. They tend to be quite expensive, or difficult for a typical consumer to use properly.
Another, and the type of thing that I think you are talking about, is to use an artificial wetland as a huge pool filter. (Plants in these cases, don't actually clean the water - they just help to aerate the sediment blanket, which is where the real action takes place.) I think that it would be very pleasant to swim in one of these, but it would also be very difficult for an average person to operate it effectively. One problem is that they're very limited in capacity (the number of humans x hours in the pool) and require cool temperatures, so they're climate-dependent. Running the pump can be very expensive (if you're affluent enough to build one, I suppose it doesn't matter) and if the pump ever stops, the purification effect stops immediately. To be safe, it would require almost daily testing for pathogenic bacteria, and you'd have to be prepared to stay out of the pool for weeks at a time, when things go wrong. There are no quick fixes for such systems.
But I'm going to try it anyway, one of these days, because I like fiddling with that sort of thing. In my area, I think that a windmill-driven pump could save a lot of expense, during the summer. It would still probably need an electric pump as back-up.