You can reach your full cloud infrastructure from any browser, all you need to remember is your google password. No need for a terminal or ssh, a regular windows, os x, linux, chromebook or tablet will do. Quite handy.
Maybe if you own the servers.
Since they're Google's or Amazon's servers you have to be able to administer them with some set of Google or Amazon credentials. Otherwise what would you do if sshd crashed?
Kill that instance, and spin up a new one.
A wise BOFH gave a preso that stuck with me "Treat EC2 instances like cattle. When one strays off the farm, put a bullet in it's head."
Don't treat your cloud machines as special snowflakes. Build infrastructure via script.
For grins, I wonder how many root AWS creds are tied to Gmail (read: Google) accounts.