Earlier quoted context omitted.
That's incorrect. The usual way of using this service is to have backend network configured that connects your services that is not available from outside (ie you have to traverse through services to reach it). The so called "security" is just a paid feature for companies that want to use ElasticSearch but want to use it in "legacy" way because, presumably, they don't have people to design it correctly.
That's still really insecure, because it means that as soon as someone manages to gain any access to that network or any of the services on that network has a security issue your database is wide open. That means that if someone manages to get access to the. I'd say public internet with proper (encrypted) password auth is more secure than that.
Having a password adds a small layer of protection to databases that the affected app wasn't meant to connect to.
It adds some protection in that case, but the user should use best judgement if it's worth doing.