I didn't mean to imply they couldn't build something with the exact specifications you are suggesting. Now I see why you are suggesting this so it would make sense to build it.

I just have a knee jerk reaction to scoff at overly complex means of building pyramids since I believe they couldn't have solved the fundamental problems with things like "ramps" or water screws etc etc. This hardly means that what they did couldn't involve any complexity merely that it had to evolve naturally from the knowledge they possessed. It's easier to believe the pyramid was a pump that built itself than that they banded together to drag stones up ramps and then left evidence for something else.

Your system could have evolved but it would have been difficult to evolve with the simple materials they actually had available.

I like your "lever crane". It might have several possible applications.