Materialize (https://materialize.com/) is capable of performing SQL operations over a stream, using incremental calculation based on differential dataflow.
CockroachDB is a distributed SQL database, with strong consistency. I think that Yugabyte is similar.
Support for realtime changes, including queries over those changes, is better in other databases, like RethinkDB, OVSDB or Firebase.
Relational is not always the best way to store your data. Sometimes a graph model is better. Or for full text search something specialized is better. In that sense dgraph or elastic search may be better OLTP databases in some cases.
Columnar storage, like used in Vertical or BigQuery have several advantages in processing and data compression. But implementing it in PG or MySQL I think that would require almost a full rewrite.