I think Android's permission system works great. I saw Facebook's list of required permissions, considered whether these functions were necessary to provide the service I needed and whether I trusted Facebook to manage them for me, then declined to install the app.
You will still be tracked on other sites you browse if you are logged into Facebook with your primary browser. That is the benefit of an app like Tinfoil for Facebook, which keeps your Facebook cookie in a sandbox.
My last phone had Facebook as one of those apps that you couldn't uninstall. I was so pissed, I've never had any sort of Facebook app on my phone nor do I want one. Even if I never signed in. Absurd.