Can you elaborate on "extra power"? A c++ constructor/destructor pair is equivalent to __enter__ and __exit__. I fail to see how this grants a significant amount of power. There's certainly differences, but the gap is probably not as large as your weasel words make it out to be.
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__.
with self.lock:
self.do_stuff()
In that case, I would say that the context-manager is nicer.