To be clear, I don't think this is a failing of open source. The problem is that Google allowed phone manufacturers to release practically anything they wanted based on the Android code base under the name "Android" and to ship with the common market (Google Play).
Frankly I don't think they should have allowed any modifications, making Android closer to how Firefox is distributed. (Anyone can edit the source code of Firefox, and even release a fully built binary based on that edited code, but you can't call it Firefox.) Maybe fewer manufacturers would have bought in at the outset, or maybe some would have tried to fork Android, but it's easy to forget what a desperate situation they were in. Outside of Apple and maybe Blackberry, the mobile OS market was in shambles because nobody was ready with high quality smartphone software. Android was a huge win and probably saved multiple companies from bankruptcy, and I think they would have eventually bought in to a more strictly defined OS out of necessity.