I don't even like docker, but it still doesn't sound that terrible to me. It's an option. Use docker or use the single binary, but presumably if you like docker and have it set up for other things, you'll just use that rather than rolling your own startup scripts etc.
I do something a bit similar for my own project - it's a single binary REST server, but I still package it up with dpkg-deb and deploy that to a private apt repo so I can update it easily on the servers with "apt-get update && apt-get install blah" and that fits nicely with my existing processes and I can just add the repo and dependency to my cloud-init setup. If I used docker, I'm sure I'd find his docker image the easiest path to getting it installed and updated.
Consistency is key. it's easier if you're using docker to run all the things, then docker ps shows all the things running, instead of having to check docker, and then also check this other thing over here that's different
Hold on, I'm back to my earlier comment.