Even if urine was not unhealthy if coming from a healthy animal, I still don't want it in my swimming pool. And most human bodies are very heavily toxic and frequently if not constantly discharging all sorts of poisons.
Still, I think I would choose that over the chlorine.
I'm not sure what I think about the purple turning chemical. It's probably not a healthy thing so it's dubious whether that will reduce or increase water toxicity.
It's interesting what the researchers said about urea mixing with chlorine to form something even more toxic than chlorine itself.
We should however consider that urea is also present in smaller quantities in sweat. So that poses more problems even.