Kaiser actually has several plans: if your company offers multiple plans, make sure that you review them all. About 10 years ago (back in the mists of time), my employer had an obscure Kaiser plan where it would actually pay (about 70%) for non-Kaiser, out-of-network doctors. It was called "Kaiser Small Business" or "Kaiser PPO" or something. So, not all Kaiser plans are the same.
People who hate Kaiser hate it because, for most plans, Kaiser only pays for doctors who are employed by Kaiser. So, if your doctor leaves Kaiser, you have to change doctors. If you change jobs, lose your job, your employer drops Kaiser or for some other reason you are not in Kaiser anymore, you have to change doctors. But don't be too scared by this. Lots of good doctors spend long periods of their careers at Kaiser and lots of companies have Kaiser plans so you have a good chance of finding and keeping a good Kaiser doctor. You just have to be prepared that, someday, you might have to change doctors.
My wife didn't like Kaiser for various reasons. One, she didn't like having to insist on being given good care; like others have said, if you insist, you'll get it but she got tired and annoyed by always needing to insist on it. Two, she's extremely picky and she's happier to choose from a broad range of doctors out there rather than only Kaiser doctors. Three, she likes knowing that if her current doctor changes employers, she can follow him to a new employer (and will probably still be covered). This actually happened and we easily followed our doctor to his new employer. Four, when our son needs surgery (like now), she wants to be able to pick the best doctor, not the best doctor that works at Kaiser. It is very comforting for her to know that all the doctors, even the ones working out of famous children's hospitals, are covered and available.
That said, if times become tough for us, she'd probably go to Kaiser again.