Carthage is a slighlty special situation. Its adjacent cities on mainland Africa trade by land..not by sea. Port blockades dont stop land trade.
As you saw though...blockade its city on Lilybeam and it cuts sea trade between Sicilly and Africa. Blockade of Islands are particulary harmful to enemy income.
Blockades might improve your own income. A third faction might now send its sea trade to you because its trade cannot get into the blockaded port.
Carthage, perhaps more than any other faction, does seem to pump out looks of cheap low quality troops. How often has Palma been garrisonned by a big stack of town watch? Not sure this is just down to the income/blockade situation.