While this is nice, I could never use something with such high latency for editing code or interactive sessions. You've just added latency all over the place. Delayed input and output plus networking across the world.
Remove the extra step going from Phone to Chromecast (plenty of phones have HDMI OR the Chromecast can run an SSH client) and this a great solution with minimal latency. Anything remotely comparable in the 80s/90s would have been totally out of reach on a student budget.
Serious (I hope!) question: how does one run the SSH client on the Chromecast? Are you proposing installing Linux on the Chromecast, or is this something available out of the box?
Totally agree with your point about HDMI, I overlooked it because my phone doesn't support it.
You can cast your whole screen from Android or a Chrome tab to Chromecast (now called Google Cast). That includes any SSH client you have running there. (There are SSH clients for both Chrome and Android)
If you look at my GGP comment, you'll see that mirroring to the Chromecast is what I initially suggested. I was specifically asking about the statement "OR the Chromecast can run an SSH client".
I suggested this because I've tried it, and it works well if you have no privileged reference frame to which you're comparing it. A new Precision with a Xeon and 32GB of ECC RAM is nice. Not necessary for the vast majority of development jobs.