I see both sides of this, but on my own team, where we are all meant to be experts on the project, I really like to be able to see the experiments, because there's a reasonable chance I'll be trying something similar to or perhaps inspired by those throwaway experiments at some point. I think there is a different trade-off in open source projects, where it's more helpful to have a history that isn't confusing to newcomers.
I think I wasn't clear. I like to be able to see completely experimental entirely thrown-away approaches in branches like you suggest, but I also like to see the little hints of partial experiments that a "dirty" history shows. My point is that on projects with focused teams where everybody is or should be an expert, literally the more history I can access, the better. Things like "did somebody already try and fail to refactor this class? What was there approach? Can I actually do better, or am I just headed down the same rabbit hole?" are invaluable to me, and the best way to answer those questions is to see "dirty" remnants of things people have tried and un-tried in the history. History can be forensics, and in forensics you don't want things to be "clean".