But you can always root your phone and install Cyanogenmod from scratch, right? Agreed that this is not too trivial right now because of standardization issues, but it could be done if you really care about privacy.
Not all of CyanogenMod is free software (you still have a bunch of binary blobs, and everyone has to use Google Play Services anyway because every app seems to implicitly require it). Replicant would be a much better alternative if it actually supported anything newer than 2G.
> and everyone has to use Google Play Services anyway
This isn't true. You can stick to app repositories like F-Droid and use Raccoon to download Play Store apps via your desktop without using a Google account on your phone.
It is true that you can get Play Store apps without a Google Account, but the Place Services framework does a lot more than this. Many apps rely upon the framework for certain pieces of functionality from Google's libraries.
Many Android apps include the Google Play Services framework in themselves, as they provide extra functionality that is not in the baseline Android API, e.g. a JSON parser.