[threeseed]

Why couldn't Google just have a shared key stored on each of the user's devices ?

The shared key could be backed up to Google's servers and encrypted using the user's password so in the event of a new device/flashing the shared key could be re-downloaded.

Then you only ask the user once for their password.

[enginous]

Encrypting anything with your Google Accounts password doesn't really make you invulnerable against Google. They can get your clear text Google Accounts password from you any time they want by just reading the password you enter on any of their clients.

[shawnz]

Here's the problem with encrypting via the account password, directly or indirectly:

Google gets subpoena'd for your data. At next logon they capture your password and grab the key. There goes your data, including your wifi password or whatever else.

Of course I don't think that this would ever happen, and even OP's complaint is a bit unnecessarily paranoid in my opinion. But there's your answer.

EDIT: However this might be plausible if the stored key was also encrypted with some sort of passphrase or PIN that was not known to Google, which I believe is how Chrome does it currently.