Not much. I consider Google to be one of the least offensive players in the category. Besides, using another provider to handle your data exposes it to new risks. Is the other provider actually more privacy preserving? How's their security track record? Do they have a sustainable business model that complies with providing better privacy? Are they burning free money? Whose money are they? Is there anything preventing them from doing a 180? Are you paying for it? Who are their investors? Etc. 🤔
Self hosting using open source software is a real alternative but it's far from trivial and therefore not available to most but the more knowledgable technical people. It requires significant work even when automation is used and security can be botched fairly easily. If the data leaks, privacy evaporates. I run a lot of self hosted services.