What if we treated Postgres like SQLite?

I think this is a great idea for testing. MSSQL has LocalDB which is used a lot throughout the .NET ecosystem:

https://learn.microsoft.com/en-us/sql/database-engine/config...

For heavy duty production use (i.e., pushing the actual HW limits), I would feel more comfortable with the SQLite vertical. Unix sockets are fast, but you are still going across process boundaries. All of SQLite can be ran on the same thread as the rest of the application. This can dramatically reduce consumption of memory bandwidth, etc.

Memory bandwidth I don't worry about much - most of the time you should settup a small database with just enough data for that test, which hopefully is fast. However sockets and processes are a worry as starting as there are places things can go wrong not related to your test and then you have flakely tests nobody trusts.