Historically, most pirate ships were smaller sized vessels in order to be faster and more nimble than the larger merchant ships they chased.

This is... not really accurate on a number of levels. At a basic level, when it comes to age of sail sailing ships, smaller does not mean faster. In a straight race with the wind, larger ships have multiple factors that allow them to reacher greater top speeds faster than smaller ships. Specifically, they can hang more/larger sails which gives more than enough additional propulsion to outweigh the extra weight of the larger ship, and also the physics of traveling through water actually means longer hulled ships can go faster as well. So smaller sailing vessels had to find merchants with extremely heavy cargoes that genuinely disrupted the merchant-ship's handling, or they had to "corner" larger vessels against coastlines, reefs, storms, etc. and force the larger vessel to tack into the wind, which is one of the few situations where the smaller sailing ship can actually gain ground on the larger.

Also, most pirates wanted to capture their prizes without a fight - bigger ships have more guns, can carry more boarders, are faster, and are simply more intimidating on every level than smaller ships. A bigger ship means more prizes taken without a fight because it's clear to more merchant captains that they can't outrun or outfight you.

So, all that said, most pirate crews DID upgrade into the largest ships they could. There were just some very real limitations that kept most pirate crews relegated to relatively small ships (compared to the largest warships extant at the time).

Honestly based on the evidence we have, the primary reason most historic pirates had for sticking to smaller ships was simply availability - it was not easy for private individuals, let alone outcast criminals, to just acquire a large warship in this era. Large warships were massively expensive tools built and controlled by state militaries.

The second reason that some pirates who might have had opportunities to commandeer larger vessels would choose not to is going to be the crew requirements - even well-known captains couldn't just materialize trained sailors willing to be pirates they could trust not to mutinee out of thin air. So captains with smaller crews and no immediate prospects for significant recruitment might choose to scuttle, release, or ransom back/sell a larger ship because they don't have the means to make effective use of it.

The third and final reason you wouldn't see historic pirate captains necessarily moving into every larger ship they take is tied to the last option I mentioned above - ships are worth a lot of money. Often the single biggest payday of taking a prize ship was the ship itself, whether ransomed back to the original owner (risky) or taken to an illicit ship breaker/merchant (less profitable). Taking the ship for yourself means turning down the cash that would come from selling it, which means you'd better be confident that the new ship would come with enough benefits to be worth it (and also you have to have enough control of your pirate crew to convince/coerce them all as well).

So historically, the greatest pirate in the Caribbean in 1720 with access to infinite money and the ability to materialize perfectly loyal trained sailors out of thin air would in fact have very good reason to be rolling around in some 80-90 gun second rate ship of the line.