What exactly happens in a bleach bath?

[LongHairGuy]

As some of you know, there is that method called bleach bath, helping worn and tangling wigs become "like new" again. Following precise instructions (there are many youtube tutorials around), it actually splits in three steps:
1. dripping the hair in a cloth bleath water solution (and rinse clear thoroughly)
2. dripping the hair in a ammonium water solution (and rinse clear thoroughly)
3. shampoo (?) and deep condition the hair and let it sit (some ppl prefer a micro wave oven for drying process)

After going through different of those tutorials, I took 3 totally felted, dull, and heavily tangling wigs on which I had tried everything else and nothing had worked (2 of them had been pruchased cheap, 1 of them was medium budget). I might have varied reaction times slightly among the 3 wigs, but in the end, the 2 cheap wigs were "somehow better, but not super-good... maybe they had been damaged too far", and wig no. 3 (mid-budget) was quite wearable again - for me it was like a miracle, an improvement on all 3 wigs, I had given up on them before.

But can someone tell me what exactly happens to the hair when going through the chlorine and ammonium baths? I ask because I'm currently (like always short on money) ordering new wigs at lowest bugdet prices. They all have one initial problem in common: Although style and quality looks perfect when they arrive, even the very first contact with water immediately turns them into a messy ball! (On a brand new hair system!!!) That means, I would never ever be able to shower, or swim with those wigs. I'm even afraid of getting into the rain. (When shampoing it, it's always an annoying act how everything tangles at once, using loads of conditioner to get it smooth again).

So, I ask myself (or better: I ask you people) should one try a bleach bath on a brand new system? Does that somehow remove the cuticle (if it hasn't been removed already) and avoid tangling from the very start? I mean, there must be something which makes the (new) hair tangle so heavily as soon as it gets wet.

So what is the actual reason on the hair surface why that bleach bath works and makes the hair smooth again?