Definitely, the bias is familiarity, as it usually is. I started my webdev days when Firebug was big, so FF was my main browser. Then Chrome came, and besides being a nice browser, its dev tools had the same familiarity of Firebug's. IIRC, FF's default tools, for some time, were different than Firebug's and I think I just liked not having to fight with the FF defaults over time (as I moved between machines frequently).
As for my class, yes, I'm not enthusiastic about shelling from the browser no matter how many people like it. But the main mitigation is that the class work we do is based off of my AWS setup: I spin up the EC2 instances and I manage/distribute the keys. None of the assignments require using their own personal info. And another reason for teaching them how to use browser profiles (something I've never seen students have set up) is so that they if they want to build something with Twitter's API, i can strongly advise for them to make a fake account and operate it in a different profile, to prevent accidental Twitter snafus (among other problems).
Why Chrome shell over PuTTY? I remember struggling with things like copy and paste, to the point where I think it is easier to use the mouse...but I push students pretty hard on using the mouse as little as possible. Chrome Shell feels as close to the OSX Terminal with the exception of key handling and the inability to access or transfer files from your own system.