Healthcheck fail fast feature during container start up

I have identical question as posted here Healthcheck fail fast feature during container start up · Issue #6751 · docker/docker.github.io · GitHub (closed because it was asked on wrong github repo I guess).
From original post:

I can imagine helathcheck scripts that could be written to detect some early unrecoverable errors like service unavailable 503 (still deploying, there is still hope) vs 404 (not deployed, and probably won’t be). I just don’t see how this additional info can be passed via current healthcheck API which only allows for 0 (healthy) or 1 (unhealthy).

So is there any way to achieve this in current healthchecks?
If no, then are there any chances for this being accepted as feature request ?