Of course the sudoers file also allows you to bind to LDAP too, so you can actually store the entire ruleset in a single location to be used by all of your systems without any 'configuration management'.
LDAP gives you some other features that typically come with configuration management too, like auditability of who made changes and when, as well as the ability to store diffs as changes and go through an approval process.
Everybody hates LDAP for reasons.. But its fine. Its good actually!