That's true.

For example, in the case of PostgreSQL, there is already a tool called pg_isready [0] to do this inside a healthcheck as you described.

services: postgres-db: image: postgres healthcheck: test: ["CMD-SHELL", "pg_isready -U postgres"]

  application:
    image: image
    depends_on:
      postgres-db:
        condition: service_healthy

However, this is not the case for other databases/services.

[0] https://www.postgresql.org/docs/current/app-pg-isready.html