Can't change Game Center nickname for existing Apple ID

I want to change my nickname in Game Center. I chose poorly and I hate it. I followed the step-by-step instructions here: How Do I Change My Name In Game Center? - Apple Community they just. don't. work.

When I attempt to change the nickname, I can clear out the existing value. It even teases me with alternative suggestions like DisappointedUser394 or FrustratedDope1927 but no matter what new nick I select—whether one of my own invention or even one of the awful suggestions—it immediately reverts to the existing value the moment the text field loses focus. Is this simply broken or broken as designed?

Many thanks...