Currently Autopromote performs an edit count lookup for user on each permissions check, even if no autopromote groups actually have an edit count condition (at https://github.com/wikimedia/mediawiki/blob/master/includes/Autopromote.php#L180). It may be worth considering skipping edit count lookup if edit count condition is 0 - it can spare quite a few queries with minimal effort, especially since edit count lookup may also trigger DB write.
On Wikia, implementing this logic for edit count lookup (https://github.com/Wikia/app/blob/dev/includes/Autopromote.php#L121) saves ~400k SQL queries per day. While Wikimedia's setup is notably different, this may nevertheless be some low-hanging performance fruit for a Wikipedia-sized project.