NoSQL has been and continues to be hugely influential. All major cloud players provide document/object based storage, as well as other NoSQL Solutions. The term "NoSQL" was dumb and overhyped... But I think it's really about using the correct storage solution for the job.
Non relational data should be stored in a non rdbms. Key-Value stores like Redis are immensely useful as caching layers (but they offer so many more features). Graph databases can be used for data with complex relationships that are not easily modeled. They are also good for seeking strong correlations between related items. (think person A. called person B. called person C. (palantir type searches).).
Searches can be done way more effectively in a specialized index, like an inverted index used by lucene/elasticsearch, which also supports things like stemming, synonyms, and numerous other features. These are all "NoSQL" NoSQL is not just mongodb (which isn't nearly as bad as people make it out to be btw).
Even traditional RDBMS are seeing an influx of NOSQLesque features. Like JSON types and operations in postgres.
The reason "NoSQL" dbs got popular are because in my experience monolithic large relational databases are hard to scale, and manage once they become too complex. When you have one large database with tons of interdependencies, it makes migrating data, and making schema changes much harder. This in my opinion is the biggest issue (moreso than performance problems associated with doing joins to the n-th degree., which is also an issue.)
It also makes separating concerns of the application more difficult when one SQL connection can query/join all entities. In theory better application design would have separate upstream data services fetch the resources they are responsible for. That data can be stored in a RDBMS or NOSQL, but NOSQL forces your hand in that direction.
As it goes for serverless, this just seems like a natural progression from containerization, I'm interested to see where the space goes.
Personally I think it's foolish to put your head in the sand when the industry is changing, or learning new concepts.