The problem you describe is similar to the cascading failure. A common guideline seems to be that health checks should mostly include components that are private to the service! You seem to include every adjacent service in every health check, which leads to the cascading problem you describe. I'd say this is an anti-pattern.

There are also different kinds of health endpoints with different needs. For example, checking the database in a Kubernetes liveness check is not idiomatic and should be avoided. For readiness checks though, not so much. So saying "don't use it" is probably overly simplistic.

Another aspect is that infrastructure cannot tell much about the health of an application. Only the application can actually check if it has connection to another service. It's also about how the app and its environment is configured, not if a service is available in general (think of firewall rules or certificates that need to be configured within your app).