This can already be done using UV light possibly combined with ozone treatment.

I'm not sure what the hydrogen peroxide method brings to the table compared with UV/ozone (besides a university press release).

[0]: https://www.espwaterproducts.com/ultraviolet-uv-systems/

[1]: https://www.socotec.co.uk/media/faqs/faqs-ozone-water-treatm...

Chlorine in the water provides disinfection all throughout the pool, this is very desirable when you have a pool. Imagine you see someone's bandage floating next to you in the water! Do you want to wait for the water to be pulled through the filtration system to get cleaned up? It typically takes a pool pump many hours to bring the full volume of the pool through the filtration system.

By having the disinfection agent spread through the pool, any bacteria or other contaminant will be acted on immediately. Algae is another big problem in many pools. Oftentimes there is some corner of the pool (or ladder, etc) that will harbor a little bit of algae that is waiting to take over the rest of the pool. Having chlorine dispersed through the water is very effective at preventing algae. Also, shocking the pool water with high levels of chlorine is oftentimes needed to keep the algae under control.

The common approach for making a pool need less daily maintenance is to get a salt water chlorine generator. A small amount of chlorine is generated by running an electrical current through electrodes. The electrodes need to be replaced every so often. Liquid chlorine is generally considered to be cheaper, but requires a lot of diligence because the chlorine dissipates pretty quickly.

I've seen hot tubs that use ozone for disinfection but not pools. I'm not sure what makes it a reasonable choice for hot tubs but not pools. Ozone would disperse through the water like chlorine, but it dissipates even more quickly.

One more interesting tidbit I picked up alone the way: the chlorine smell in a pool is not from the free chlorine. Free chlorine is what's available for disinfection. After a free chlorine molecule bonds to it's target, it's called combined chlorine. Combined chlorine is what is responsible for the nasty smell in pools. The solution for combined chlorine is to add dd more free chlorine!