I don't say that asyncio gives you nothing! Go for it with your DB access if you have already gone async in your design.

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.