And if Chaos corrupts some Time Lords, then their power is added to Chaos. They too, can play it smart.
Define "some Time Lords". The Transduction Barrier around Gallifrey could fairly easily no-sell Chaos corruption, or even the shielding on a standard TARDIS (both have "dimensional shielding" to stop reality-warpers, even universal-level reality-warpers, from fucking with the occupant or the machine itself), and while I could see some rogue Time Lords like the Rani, the Master on a bad day, the Monk or even Morbius falling to Chaos, they're not exactly going to take down the rest of the Time Lords on their own, are they? There are also some Time Lords who are really, really good psychics. Take for example Salyavin (was stated to be capable of mind-raping everyone in the material universe at once, though thankfully he turned out to be quite a nice guy), or Omega (created a universe with his mind and sustained it long after his physical body had decayed away), and that was without a TARDIS or any other form of technological assistance.
I have no idea dude, I don't actually watch the show. But if there is temptation to be had, then you can bet the gods will exploit it, and if they are nerfed in comparison of a sue-fested universe, then they'll play the long game, and wouldn't reveal themselves until they've got their own rape train ready to put the screws to whoever poses the greatest threat.
Well fuck, now I want to read a fanfic about a Chaos-corrupted Morbius building up another giant death army made up of another amorphous horde of screaming, power-mad fanatical humans and aliens, but this time they have Chaos magic. CANADIAN, YOU'RE MAKING ME WANT IT MORE! Well, there was this one fic I read a while back about some pre-Time War and pre-Apocalypse Element Daleks crossing over into the WH40K universe and encountering Chaos, that was pretty good. https://www.fanfiction.net/s/8553139/1/Corruption-of-the-Daleks I'm gonna read this again.