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.

Stop arguing from extremes. A $300 notebook is better to code on than that phone-tv-remote-machine-via-ssh setup. For a start, you can use an IDE that isn't terminal-bound. You can also code at a desk (or wherever) instead of tied to wherever your TV is, at watching-the-TV angles and postures. You're also not going to lose your session and potentially your unsaved edits because the network interrupts. Yes, you could use tmux or similar, but now you've changed the standard keyset (and screwed normal scrollback), and are increasing the requirements to entry.

A cheap notebook is also a much lower barrier to entry - in order to have your own droplet, you need to know how to set up a cloud machine and connect to it properly. That's not trivial knowledge to a newbie (nor is it relevent, unless they're coding for servers), even though us old hands can do it in our sleep. Similarly, you need a way to pay for for the online subscription.

Laptops are not exactly heavy these days anymore