Part of the appeal of ChatGPT compared to traditional writing assistant/grammar checkers is that you can tell it to write in different personas, although IME it's pretty spotty at this still. Lots of conversations that turn bland and repetitive quickly if you don't get lucky.
I'm not too worried about "default GPT style" becoming common, though, because I think it's more likely to be used by the people who have no style beyond "what I see on TV and in my family." Raising the floor, basically.
Anyone who wants their writing to stand out will still have to differentiate themselves. To put it another way: you're gonna be able to recognize the lazy users pretty quickly cause they're gonna have "GPT voice."