If a governor has traits that have a negative impact on trade/tax/mining/farming income etc, and those negatives outweigh any positive bonuses he may have, then it's possible for the settlement to make more money without him.
Obviously good governors with good bonuses are preferable, but sometimes the biggest impact on income can just come from the placement of your capital. The further away a settlement is from the capital, the more corruption occurs, and if you place the captial far from the more profitable settlements, you end up losing money. In a Roman campaign, the moving of my capital from Carthage to Sardinia (or one of those islands near Rome) brought in an extra 6K a turn - that's not to be sniffed at!
If you do have a governor with high management skills, (and hopefully some other good traits/ancilliary characters) definitely stick him in charge of your richest settlements though. High management skill alone can bring in an extra 1000+ denarii a turn. Money gained through management skills shows up on the settlement details screen as 'administration' or something like that.
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