Simple to implement.. but you're kind of requesting a "let me know if my server packages need updating" indicator.
What will people request next? Kernel version? Version of other apt packages?
I'm sure we all are logged into our servers all the time for other operations (apt updates, monitoring, auditing etc). Checking docker version while doing that is trivial, and you should be checking more than just docker.
What would showing you the docker version solve? (you said: ".. it would be a good solution..")