In my opinion, I don't think it's worth much and It doesn't seem old enough to be a collector's item. Tho it could be as the nameplate ratings are in fairly old terms that I haven't seen in several decades which can definitely date a man. Sweep 56 inch, 110 V.A.C., 50/60 CYC.
Your controller is called a step transformer speed control, they were nothing special and primarily used because of the higher amp loads of larger fans back then and also they didn't inject all the line noise and hum into nearby electronics (radios) like early dimmers were notoriously known for.
Also, just google "bakelite test"
Here is one I found that is quite a bit newer than what you have.
https://www.ebay.com/itm/VINTAGE-CHADWICK-CEILING-FAN-WALL-5-SPEED-MOTOR-CONTROL-NEW-OLD-STOCK/23351...