That’s what OpenAI is doing.
In the terms of this service they explicitly reassign rights of the output to the user. So implicitly they believe they own the rights and are legally able to reassign them to you, a user of their service.
In my view they do not own those rights originally and thus are unable to resign them.
Google gets a pass because nobody is suing Google. When people try to sue Google, Google simply stops indexing them and then they start begging Google to infringe their copyright again.
Just because people having been posting memes and reposting pictures and comics with cropped credits and pirating stuff that doesn't mean any of this is legal.
Legality isn't about what you can technically do thanks to how the computer works, or how HTTP works, or how the laws of physics work. Legality is just about what is law and what is not.
Redistributing copyrighted works without license has always been illegal. People don't get sued for it all the time because it isn't worth the hassle and most small time copyright holders simply lack the resources to pursuit action against random Internet strangers across the Internet. That doesn't mean they don't have a copyright, they merely chose to not exercise it. And that's not a W for technology. That's literally just more abuse than a person can cope with. It's an L for society. That's like if you started getting so much spam in your e-mail that you gave up marking them as spam. That doesn't make them not spam.
For example, if I wrote something in my blog and someone made a scrapper that reposted it entirely in their website full of stolen posts, I could take legal action against them. For a blog post. For something I wrote on the Internet. That's my right. But imagine how much time I'd have to spend to do this. It would be easier to check if Google has a way to tell someone stole my content and just get them delisted from Google than going through legal channels.