I'd like a service like this, but which I could just SSH to and automatically connect to a fresh Linux instance each time.

It seems like it'd be pretty simple accomplish. You could continually pre-boot a number of Linux containers proportional to the amount of traffic you expect. When a user attempts to connect via SSH, just pop them into the next available instance, FIFO style.

Users could either log in as 'anon' with no password, or they could pick a username and then set up an account just by SCPing their public key, allowing them to persist their instance or save the state for later.

Come to think of it, I basically just described Google Cloud shell, which I really never use, but maybe a lite version with a very simple usage model would be more desirable. I know there's also Docker, but I think the appeal of this idea to me is that I don't need to use any of my local system resources, and I can log in instantly rather than waiting for a container to spin up.