I have some ideas. Here we go:
"Named ships" from famous pirates could be captured and used, as long as it would be harder to win the battle if we compare with normal ships. Some requirements could also be implemented to make it more fun like the need to win the battle over a melee fight and at the same time don't damage the hull more than X%. The player could use the ship on his own fleet.
Normal ships could be captured for profit only, to be sold for a small amount of gold if we compare the sale price from a ship we bought and sold, but at the same time, to be able to sell the ship, it would need to be 100% repaired, so if the player damage the hull to much, it would not render him profit, so he would need to capture the ship taking care to not destroy/damage to much it. If a ship is not worthy to be sold, the player could choose to dismantle it and try to salvage few good boards that could be sold on the market or even used to repair his own ship.