I want to agree, but website passwords are a usability nightmare for mobile users. Take all the hassles that come with sites having eleven million mutually incompatible sets of requirements for passwords, and throw on top of that that typing them on a phone's keyboard is slow and error-prone. Only password-compulsive geeks are going to go for that option. Your average user won't. For them, it's a huge con.
I agree that it's troublesome that people have their phones set up so that anyone with physical access to an unlocked phone has access to everything. But I'm inclined to think of that as a symptom of the problem rather than the problem itself. The root of the problem being that too many folks who draw up security schemes don't seem to grasp the most basic lesson about how people deal with security: When given a choice between excessively inconvenient security and no security, your average user will always opt for no security. If that's not an option by default, they will figure out a way to make it an option, and then opt for it. (Sticky notes, y'all.) If there's no way to make it an option, they will go find someone who lets it be an option, then opt for it.