I understand the point if you're already proficient with PG, and want to keep it in the same system. But I will say Elasticsearch is surprisingly easy to get started with. Install, POST some docs, GET a search query. That's pretty much it. I implemented it for a project and it literally was a few hours to get rolling with it (and improve search speeds by orders of magnitude).
But sure, it is another system to have to deal with.
While it's definitely easy to get started with ES, I've found the tedious part to be ongoing coordination between two systems. Unless there's no interaction at all between the documents stored in your search index and the data stored in the database, it is necessary to coordinate them at the application layer, which is more complex and can be less performant than doing everything in the database.
But sure, it is another system to have to deal with.