It does have minor disadvantages, abandoned sessions need housekeeping (a crontab job may work for you), UDP is sometimes blocked in corp/uni firewalls, SSH agent forwarding is tied to first connection (can be worked around), X forwarding doesn't work, I also wonder if the local echo for example using vim causes more burden that it solves when say not in insert mode in vim. Other than that mosh is great especially when mobile or switching between VPNs etc..
It's not a SSH replacement - X (and port and agent) forwarding or file transfer are different features. Mosh is a remote terminal client (and an absolutely brilliant one!), whereas SSH has a lot of different applications besides this one.