Google is a public company so its shareholders want the stock price to be higher ASAP. Being an unquestionable leader in AI with a product as good as ChatGPT (and maybe an image model available to the public) would help in that goal.
I really don’t think it would. Google is already number #1 in search. OpenAI is quoting a ~$40 price per month for ChatGPT Pro right? That’s not an insignificant cost for 99% of the population. I don’t see how it makes sense for Google to release something until they actually need to.