Yep. However, another important piece to remember is that Hades was the only sub-routine that was built with the ability to take control of Gaia. However, Hades protocols with Gaia keep it in check. Once it is corrupted, it no longer cares about the balance it shares with Gaia, and begins to take control out-of-turn like Travis worked so hard to avoid in his coding.
Yeah. Gaia warns that everything will go chaotic without her. Each sub-routine will continue to operate without her, but independent of one another. Before the corruption, Hephaestus would work as a part of Gaia to know it should build this or that, but without Gaia it completely runs on its own without an understanding of the other pieces. That's why it eventually starts building weapons on it's machines, because it can't coordinate with Gaia---it perceives other functions of Gaia, including the humans, as a threat.
I think as far as Gaia was concerned, Earth was habitable enough. At Zero Dawn, no human could even go outside without a suit on to breathe. When 300 years had passed and humans were let out due to shortage of food, the Earth's biosphere had been repaired by quite a massive amount already (I would consider) since they could go outside without a suit, animals existed, and machines were peacefully fixing things up still. As for purging Hades...yeah. The Hades sub-routine altogether doesn't make much sense to me in terms of being made....I'm with you that if I were Gaia, and I see things have gone well, humans can breathe, life is growing, I would wipe Hades out. However, I doubt Gaia could for some reason.
When Hades was running, yeah. Gaia was kept on the backburner. Hades had to be properly programmed to hand control back to Gaia when it completed it's task. What I loved is that Travis said some versions of Hades were too weak, and Gaia would pretend it wasn't in control, but was secretly manipulating things behind-the-scenes like you mention. That's a pretty damn smart AI. However, I think what Salamando is asking is why Gaia didn't purge Hades when Hades wasn't in control at all. When Gaia was running things, and could see life was growing properly, why not delete it then?