They also didn't release Imagen which doesn't seem to pose any particular threat to any of their existing businesses. And doing a ChatGPT style demo would also not have posed any threat to their business for the same reason ChatGPT itself doesn't: you can make it available for a while, get loads of attention and then paywall it until you figure out a better approach.
The PR threat seems overblown. OpenAI isn't suffering any obvious reputational problems from making models available to play with, because people understand that AIs and their creators aren't the same thing.
Also, though OpenAI is mostly a collection of really cool tech demos that may or may not turn into a business, not releasing demos like them is a major strategic blunder for Google. If you're an ambitious AI researcher where do you want to work now - the place where your work will get put out there in front of millions of people and become an overnight sensation, again and again? Or the place where your work will be put in front of, at best, a bunch of Googlers, and the only public knowledge of its existence comes from leaks and a web page saying "we can do that too"? Unless Google makes a vastly better offer than OpenAI can, it's going to be OpenAI.
They've made this mistake before, with the cloud. Years ago, even before AWS existed at all, Borg and related tools were vastly superior to any publicly available cloud system. When I worked there we repeatedly asked management why that wasn't being turned into a business because it was so damn obvious that there was massive value in what had been built. The answer was always that Google could always make more money by keeping its tech private, because ads was such a great business model. That take ... didn't age well. They lost their chance to define what cloud meant and now GCP is lagging in third place.
Unfortunately for Larry and Sergey I think the reason they aren't keeping up with OpenAI is actually not business model related, which is why they're going to have a hard time fixing it. They actually told us why they aren't releasing demos already and there's no reason not to take them at face value: they believe AI is literally dangerous and "unsafe" to release.
It's been apparent for some time that there's some sort of weird internal purity spiral going on inside Google. Imagen is only available to employees yet, apparently, has been filtered so it refuses to draw people. If you want it to draw a person-like thing you have to ask it to draw robots. That's not a business model concern. The rationale appears to be some sort of DEI maximalism: if you asked it for people it might not draw the right kind of people, that would make Googlers/people racist, and so we have to block that. This reasoning seems largely unintelligible from the outside looking in, especially in parts of the world where these topics are less emotionally/historically charged. It comes from the kind of ultra-transitive worldview in which one person says something, or allows some words/images to appear somewhere, and someone else who may not even have been exposed to those words/images does something bad, and it's therefore the fault of the first person.
Google's business model was once summed up by the mission of making the world's information "universally accessible and useful". I'm not sure they still believe in that, or at least not enough of them do. If Larry and Sergey want to get their AI products out there they're not only going to have to tackle thorny business model issues, but also try to reset the culture to the old one. The one that looked towards an optimistic future in which advanced technology could empower everyone, regardless of who they are.