It's built on the same technology as FIDO keys, so if you want to take control of it yourself, just use a hardware key.
Now, why are they doing it for free? Why take on a huge responsibility for no money, what do they get out of it?
Fortnite even has a free dance that you can only get by enabling 2FA.
Like this isn't particularly different from me backing up my (encrypted) disk which contains my (further encrypted) keys to the cloud somewhere.
What is concerning about giving encrypted keys to someone? If I give my encrypted key to you, right now, I retain control of my data. One of the fundamentals of encryption is that you can freely share the ciphertext without giving up control of your data.
That's kind of the point. We have to trust that Google won't mess things up and we have essentially no recourse if they do.
It isn't fair to presume that everyone shares your lack of knowlege on a subject, and it's simply incorrect to presume that because you don't understand something that it cannot be safe or reliable.
