I wouldn't call it a replacement, as it uses ssh for authentication and strives to not reinvent the wheel there. That is actually what makes mosh so nice - if you have your hosts in .ssh/config and your public key installed to your hosts, you can use mosh instead of ssh in interactive sessions and It Just Works. You still have ssh for file transfer, TCP and X11 forwarding, etc.

For telecommuting, it's really nice to have mosh handle handovers between wifi and 3g/4g networks so gracefully. And for high latency links, it makes the user experience a bit less annoying.

edit: missing word added