As a long time user of googles web based terminal (accessed normally through google cloud platform console by listing your VMs and clicking the SSH button):
I love it because I don't need to worry about key management and can access my machines anywhere that has a browser.
However, my few gripes are:
1)when copying text out of the web terminal window that spans multiple lines (on Mac osx chrome), newlines are inserted.
2) ctrl v doesn't work (nano/pico)
3) Ctrl c sometimes doesn't work