I don't know about elasticsearch specifically, but I'm skeptical of special-purpose systems for databases.
They are great in some cases and terrible in others, and over time, use cases push database systems into their worst cases. Use cases rarely stay in the sweet spot of a special-purpose system.
That being said, if the integration is great, and/or the special system is a secondary one (fed from a general-purpose system), then it's often fine.
I’m not sure I fully understand your comment (databases that are special-purpose and evolve out of a sweet spot, or special-purpose systems using databases in worst-case ways?).
I certainly wouldn’t say ES is the former. We use it for some conplex things that (AFAIK) no other (publicly available; I don’t what eg Twitter or Google has going on) system could provide at the scale we need. Everything we’re doing is well within the realm of what ES is built for, and it’s the only system built for it. It’s not perfect, but most of our performance issues could be solved by scaling out, where query or index optimization isn’t tractable.
They are great in some cases and terrible in others, and over time, use cases push database systems into their worst cases. Use cases rarely stay in the sweet spot of a special-purpose system.
That being said, if the integration is great, and/or the special system is a secondary one (fed from a general-purpose system), then it's often fine.