Well... The question really is "whose job is it to provide security against remote or local physical attacks?"
Chrome doesn't do RAID, it doesn't do tape backups, it doesn't patch the OS with updates. Such services and tasks are clearly something else's problem.
Disk encryption exists, if currently unusual. Locking screensavers are everywhere, if not always used.
Users have the ability, today, to protect against the attacks that a browser master lock also provide.
A browser master lock is:
- not going to be as effective (system based security would both protect against more things, and likely be technically better as its importance would get it more attention from devs and testers)
- be annoying to those using other locks (I hate the gnome keyring thing, for example. I just logged in to my account, and you want me to log in again?)