"Compose on Kubernetes"[1] seems to be what they're advocating at the moment, and it's included in Docker Desktop. It's probably an OK first step for simpler deployments, though I suspect in order to do any troubleshooting, one would have to learn k8s anyway.
Have you tried moving from on-premise docker-compose to managed kubernetes in the cloud?
If you've been diligent in striving for stateless containers that will help you - but pretty much everything thing else in your compose file is useless.
Docker-compose gets you the "pod"-level in k8s, but doesn't really help with ingress/services etc. So no one can reach your app, certainly not via a load balancer that terminate ssl for you.
This is no longer a game of "beating the nginx container until it gives up and does what you need it to".
That's assuming the existing tools (implementation). Having a spec means you can build more and new tools that do different things. I would expect docker-compose to improve or something else that implements the spec can come along and do what people need. Or, more than one thing can come along.
Oh, I didn't read your comment with a view to the future - I certainly hope a spec and further development of the ecosystem can help improve the deployment story - which would help keep the development story relevant.
1. https://github.com/docker/compose-on-kubernetes