you probably know you don't have to use a root user. You can create a user with minimum authorizations
I would probably do it for home, maybe. But creating a health check from the app I already am building and pinging that does the job and isn’t too hard. In addition that tests the secrets provided to the application. Secrets management and rotation is also a challenge!
But I can see why some people might want to ping their DB.
At work we also monitor the other way for example alert if CPU or Memory usage on the DB is high. But this doesn’t replace a ping check just augments it.
Obviously that's something every software developper could add to his own project, that's not rocket science, but after the nth project, it becomes a bit tiresome :-)
I would say health check endpoints are still very useful, and complement what you are offering here. When something is down and there is a panic (but trying to stay calm) having a barrage of checks to play the "Sherlock Holmes" game is useful.
If for example your service says "Mongo is up" but I also see "Mongo Healthcheck is down" it is probably a configuration (connection string) issue or maybe a network issue. Without your check elimination would take longer.