With Python and asyncio, neither assumption holds, but the idea of shaving off some latency persists: if we rewrite everything using asyncio, our DB accesses can be parallelized, yay! This may or may not be a net win in latency; reworking your DB access patterns may gain you more.
Nope: https://techspot.zzzeek.org/2015/02/15/asynchronous-python-a...
But often the lower-hanging fruit is doing more joins in the DB, fetching fewer columns, and writing your query more thoughtfully. Async only helps if you can do something while waiting for the DB to complete your query. A common anti-pattern, exacerbated by ORMs, is doing a bunch of small queries while passing bits of data between them in Python; moving that to asyncio won't help much, if any.
Reluctant to add a "me-too" comment but I think you have it there. For whatever reason people are much keener to investigate different ways of scheduling IO than they are to investigate what the query plan looks like and why.