I like the concept - its a fun idea. I think it would be good flesh it out with more puzzle mechanics.
I ran into some game breaking bugs. For example, the third child would not appear after my first attempt. Also, the level on the far right wouldn't pull sometimes. It might be because of all the Itch.io labels - maybe they are diverting the mouse input (not sure).
This is just a small gameplay satisfaction thing, but regarding the levers, I recommend making the hit boxes bigger than just the knob at the top. I often clicked and dragged lazily and got nothing. Personally, I'd rather connect every time than have to be careful and click/drag the small knob each time.