The rectifier also provides a signal that the assembly has completed a rotation, so you can maintain image stability based on actual position, rather than guessing how long a cycle is.
Transmitting power via induction might work, but I was never able to deliver it efficiently enough, so to make it work I had to turn up the source voltage so high that I worried about fires.
This advice comes from my 2001 Burning Man art project. A very sad early prototype is pictured here: https://github.com/sowbug/tqw/blob/master/photos/side.jpg. The final installation worked great.