The problem is when they lose their phone, how do they contact somebody without having their phone contact list. They do not have a phone to import this backup into. They do not have their phone on them to access a website with the backup. The backup ability is basically irrelevant, as all carriers can backup and restore your contacts seamlessly. It's the lack of the phone being the problem.

Presumably, we're talking about the short time-frame of a few hours between the act of losing the phone, and needing to contact somebody. The kind of situation where you ask somebody to borrow their phone.