Being able to read my email in multiple places makes my email address less capable of being a good contact point? You're right in that I always carry my phone. It receives my email.
Yes. You can only get SMSs from a single device. It's "something you have", not something you could have left logged in at an Internet cafe, or had the password sniffed when connecting via WIFI at Starbucks.
It's not used as a contact point. We don't ring you up for a chat.