Of course. They have all the data and statistics. And they have the comprehensive reach to give insurance to everyone, *for a much lower cost*. We'd be fools not to take it, because it's so cheap, and covers *everything*. Cars, houses, rentals, electronics, babies, jobs, farms... anything you have or need.
This will kill the Insurance Industry(TM) as we know it, and replace it will GoogleSure, in which you are automatically enrolled once you turn 16. Enrolled for life.
Inevitably, this imperious mission creep will eventually invade politics: first taking over all lobbying, then the politicians, then finally the entire government itself. We will become citizens of the GoogleStat. Politics, lawmaking, poverty, homelessness, immigration, budgets, subsidies, etc. all will be done in the most efficient manner possible; the entire economy will be 'tightened up' thanks to Google's efficient algorithms. And we won't even need to vote on anything anymore, because our Benevolent Father Google will already know what we choose, where we drive, how we live, and what we want. The Holy Algorithms will simply select the best laws for us, and the DriverlessGoogleCopBots will enforce them, just like Judge Dredd: Judge, Jury & Enforcement rolled into one... One Massive Algorithm to Rule Us All. And it will finally be perfect.