It is also: another server to handle, another view of your data you have to manage, another point of failure and another security entry-point.
If you don't need all the functionality of ES you can go a long way with the Postgres fulltext search. Once you scale enough or if search is your core business ditch it and deploy a better solution like Elastic Search.
Exactly. When getting started initially, it can be a huge time savings to get your basic full text experience running in Postgres directly, if that's already your main storage DB. Setting up ES is not at all trivial for the average developer and can waste a lot of precious time too early in a product's lifecycle.
If you don't need all the functionality of ES you can go a long way with the Postgres fulltext search. Once you scale enough or if search is your core business ditch it and deploy a better solution like Elastic Search.