One thing I infer from your answer is that it seems that there is an established process and dedicated tooling for working with patches at Google. I think a lot of my pain with patches stems more from the lack of process and lack of an agreement on formats and standards in my environment than from the use of patches per se.
Where I still see an advantage of branches is that they facilitate documentation of what has been done by whom and when. All of this documentation is in the same place and form as the documentation of changes in the trunk. It all is in commit messages whereas patches are only documented somewhere else, possibly in the Email or IM used to send the patch. Even if most of the branch documentation does not survive on trunk when we squash the final merge it is still there and easy to find as long as the branch doesn't get deleted. When I want to look up why I applied a certain patch I'll have to dig through my messages. I think that makes it harder to work with patches than with branches.