Is there any point setting the keys and salts in wp-config.php?

  1. If I choose to leave this up to WP, what should I actually put in wp-config.php?

Sounds like something you can easily find out. My guess: if you don’t have the define('AUTH_KEY', ..) etc. statements, the system will not work.

  1. Some sources (this SO answer, for example) appear to state that putting the keys and salts in wp-config.php is “more secure” than using the database version.

With clever SQL injections it is possible to read data from the DB, even if I don’t have direct access to it. So all I need to get the keys is one plugin that has a SQL vulnerability and I can get them.

If I store part in the filesystem and part in the DB, just access to information from the DB is not sufficient anymore.

As suggested in the other answer, just use WP’s generator or any of the other ones (e.g. this from roots.io) and supply these keys differently for each site that you spin up.