There were two "flavors" of pirates -
Psychopath thieves looking for sure thing victims.
Mercenary ex-navy or reserve navy using larger ships or sloops with enough guns to defeat smaller navy escorts and capture larger prey. They do the job for the government, supply their own ships at their own cost, and pay their own wages. Large ships cost more and are slow.
Bonhomme Richard would have been a poor choice for a French privateer -too tall too slow - just let Mikey have it.
Any sort of arty battle is the opposite of what the psychopaths wanted. They wanted relatively small - fast - carry enough crew to swam and overpower a merchantman. A sunk merchantman give no cargo or slaves to sell. Guns are heavy. Heavy is bad for speed. If the navy shows up run away - run away is the only logical option.
Compare the actual situational need with delusional modern illustrator imaginings.
I have plans for actual 18thC. cargo carrying vessels - most are closer to being a boat than they were to the Navy vessels that they supplied and were protected by. It would not take a very large pirate vessel to intimidate any merchantman into surrender if it could not flee.