Game Center removal

I have no desire to use Game Center as it doesn’t appeal to me. However, every few months, it automatically logs on, usually after an operating service update or security patch, and then I am automatically signed on again. I have to then sign off again on my devices, but good old Apple keeps prompting me to sign in to Game Center when I open an app associated with a game.

Is there a master switch somewhere which allows me to either delete my Game Center id (created well over a decade ago and never used since) or simply remove this functionality in its entirety from my algorithmic repertoire? It’s very irritating that Apple does this “automatic sign on” without my consent. (Maybe there’s a GDPR issue here? I do not know.)

Please advice. Thanks.