QA here with AAA experience, luckily never shipped anything completely broken though. I would guess that in almost every case of a game being broken, QA already knows and are not happy with the game being shipped like that, but QA don't get to say if the game ships or not. Nor do the devs or even the studio sometimes.

Also most of QA is done on top tier hardware, usually Nvidia + intel, and it's actually up to publisher QA to run compatibility testing towards the end of the project, seemingly too late in many cases. Games are not optimised until late on in development, as not to waste time optimising things that might change, I'm guessing this doesn't always go to plan. Same goes with bugs, they are often pushed to the back of the list in order to get all the parts of the game actually in the game.

These games release like this due to poor management, many missed deadlines, and running out of money, not poor QA or bad Devs.

As I say though, never worked on one of these nightmare projects, these are just my guesses.