Most people don't care about Google knowing whether they're using a particular app. If they do, they have the option not to use it. The main concern is that the chats themselves are E2E encrypted, which we have every reason to believe.
This is a perfect example of purism vs. pragmatism. Moxie is a pragmatist who builds things that the average person can actually use. If it means that millions of people who would otherwise have used ChatGPT will migrate because of the reduced friction and get better privacy as a result, that's a win even if at the margin they're still leaking one insignificant piece of metadata to Google.