For a long time, the only reason ElasticSearch was not the ugly duckling of distributed systems was because MongoDB existed. It does not have a good history at all. There was a time that Elastic even claimed that it beat the CAP theorem, which always makes me chuckle when I'm reminded of it, and historically they also have been quite vague about the distributed properties (and shortcomings) of ES.
It works fine as a secondary datastore when you would benefit from all of the implemented search functions, but I wouldn't trust it for consistency (so I guess in a way it is a replacement for mongo \s)
Not only that but having operated ES clusters before, it's a tricky thing to manage, and depending on your workload they can be very resource hungry.
PostgreSQL is very solid though, and will scale well for the majority of people. I highly recommend this over ES, not to mention it does have some search features too, you should check them out.