Anything is possible with pirates, there was one real-life incident where a pirate captured a ship just to steal the hats of the crew because he thought it was funny.  I'm not making that up, that really happened.

Real pirates always wanted to keep a ship they thought was a good one, which generally meant a fast one.  If they weren't interested in the ship, they would usually just take the cargo and allow the crew to leave with their now mostly empty ship.  Most real pirates during the "golden age" of piracy were veterans of the 7 Years War who, after the war, decided that they would rather use their skills learned during the war to live free and independently as a pirate than return home to live under the rule of a king.  Most pirates were not the ruthless killers that most believe they were.

If they kept a ship it was because it was a good one, and they had enough men to man it.  So you might make only half the ships worth keeping, and that will solve half of your issue;-)