If I understand correctly, the logging during shutdown coming out of asyncio helps debug errors in asyncio programs, and this logging can't happen before shutdown starts (so the application calling logging.shutdown would just hide the errors, I think).

Yes, the general problem affects more than just logging, and when it is reasonable to do so we try to fix (or at least cleanly report) these shutdown issues in stdlib code.  Whether it is reasonable to do so in this case I don't know.