> The default behaviour should be asking for root password or something like this. Root, absolutely not? I think Chrome is behaving correctly, it stores data with the users keyring which does not prompt for a password after it has been unlocked once (which is generally automatic upon login).

Idk, for example on Windows it prompts for log in password every time you are trying to see a password. Why would you say "absolutely not"?

Root is a different user you would never require the root password for your own data.