PostgreSQL’s protocol is currently at version 3, and there are concerns about improving the protocol in this regard.
The V4 wire protocol changes and the wanted features for V4 documents share concerns about version 4 with pipelining and multiplexing in mind. PostgreSQL also has a proposed feature called Protocol hooks that decouples PostgreSQL from the current protocol. It aims to provide extensibility of the wire protocol. Such a feature could be an enabler for multiplexing.
It took 25 years to deliver HTTP/2 and introduce multiplexing to increase performance drastically. Most database protocols have not followed the same path yet and remain in the stone age of connection pooling (at least databases with an openly documented protocol).
Multiplexed database protocols could improve performance, and make connection pools a thing of the past. It would also provide the foundation for efficient data streaming from databases.