A properly designed treadle feeder doesn't waste feed by having feed raked out and yes they do eliminate the rat problem as long as they are installed properly, the spring is replaced when needed, and some basic housekeeping is maintained. Some poorly designed feeder like the grandpa feeder or one of the Chinese knockoffs are made with no side lips or a side guard instead of having a properly designed feed tray. Full side panels with side flanged and a half inch wide feed lip extending horizontally into the enclosed feed tray prevent 99% of most chickens from raking feed out. The 1% might need a feeder lip extension to stop their feathered behinds from raking feed.
I would educate your city council about the use of treadle feeders to eliminate the rat problems from keeping chickens. You might make your local animal control department aware of the types of treadle feeders and ask if they would help approve and pass an ordinance requiring a properly designed feeder for backyard flocks. Several things are essential, a spring loaded inward swinging door, a heavy counterweight to balance the door/treadle bar/step assembly, and a fully enclosed feed tray. And no plastic, aluminum, or wood allowed. You never know, they might give you a variance on the ordinance if you let the animal control dept monitor the set up for a few months to prove that raising chickens doesn't have to mean having rats or mice taking over.