> if it encourages dev teams to stop the silly habit of returning successful health checks from their microservices even before the back-end dependencies (DBs, other web services, etc) are ready, then it might have some value

Deciding what starts when shouldn't live inside the things themselves. They should be able to start independently and react accordingly if their dependencies aren't met.

Two reasons:

Dependencies can vanish anyway, once everything's started, so it's silly to special-case starting a microservice.

Microservices can need to behave differently depending on the deployment situation, so you don't want to bake into them a single way of doing things.