I have to say that this is exactly why I like having Kaiser as my health insurance. Because Kaiser is also my healthcare provider, if I need to see a specialist, all it takes is a referral from my PCP or any specialist I'm currently seeing, and it's done. And, they practice evidence-based medicine to the extent that's possible, which means that treatment decisions tend to be pretty reasonable. My PCP refers out whenever there's anything outside her expertise.
I know it sounds like a massive conflict of interest to have one's physician working for one's insurance company, but, somehow, it really seems to work and work well, bypassing those failure modes you mentioned entirely. I've gotten in to see specialists within a matter of a couple of weeks whenever I've needed it.