Are there any cases where someone was caught cheating and promptly copped to it? I guess it’s hard to tell if that’s never happened. I’m truly intrigued.

Yes, for example https://en.wikipedia.org/wiki/Frederick_Lorz They were initially banned for life. Maybe copping to it eventually let their sentence be commuted, hard to say.

There's probably more recent ones too, this was posted here recently so was on my mind.