There are a lot of reasons why I might want to login on a computer I don't own to do something, rather than to use my phone. Having a keyboard is a major usability benefit for many types of work. Larger screen, printer. Software that is on the machine that can't run on my phone.

I agree with you; those are all reasons I only use my phone for on-the-go messaging or navigation. I'm against the idea that you should have to have a secure (against the owner) connected phone on your person at all times in order to sign in to a web service.

Thats still irrelevant to the example being discussed.