I didn't have any example of extra power, just in with blocks you have some downsides compared to RAII but no upsides. By downsides I mean that in C++ you write the constructor/destructor and never worry about it again, but in python every caller has to use a with block, plus what I said above about exceptions being thrown before __enter__.
I haven't done much with mutexes, but doesn't having it split over 2 classes introduce a race condition? Seems like a weird way to implement it to me.
You complain about having to put initialization into 2 constructors, but there's the flip-side with things like mutexes. In c++, you have to have 2 classes, one for the lock and one for the guard. Whereas with a context-manager, you have one class and the locking code is in the __enter__ and __exit__.
In that case, I would say that the context-manager is nicer.