I suspect your app is doing lots of tiny single-row queries instead of efficiently batching things. It'll be wasting huge amounts of time waiting for results. Even if every query is individually incredibly fast, with the number of them you seem to be doing you'll lose a LOT of time if you loop over lots of little SELECTs.
Using unix sockets, you can expect about 10-20.000 queries/s on small simple selects per core, which is quite a feat. TCP adds overhead, so it's slower. Over a network, add ping time.
In plpgsql code, you avoid roundtrips, data serializing, and context switches, it can be 2-4x faster.
But a big SQL query can process millions of rows/s, it is much more efficient.
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