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.
Thats still irrelevant to the example being discussed.
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.