We have everything optimized, and yet somehow DB queries need to be "interpreted" at runtime. There's no reason for DB queries to not be precompiled.
The problems related to PostgreSQL are pretty much all described here. It's very difficult to do low-latency queries if you cannot cache the compiled code and do it over and over again. And once your JIT is slow you need a logic to decide whether to interpret or compile.
I think it would be the best to start interpreting the query and start compilation in another thread, and once the compilation is finished and interpreter still running, stop the interpreter and run the JIT compiled code. This would give you the best latency, because there would be no waiting for JIT compiler.