Preface: The following is a mostly speculative answer, but one that I would argue is logical and will try and support it with other POTC-related media. The problem lies in that POTC is an ongoing franchise, which may be working towards a redemption arc for Captain Jack Sparrow and includes each film digging deeper into Jack's past and ultimately is building some origin mythologies. So there could be a more solid answer down the line.
The Black Pearl was formerly The Wicked Wench and belonged to Captain Morgan. We also learn from DMTNT that Morgan was also the previous owner/user of Jack's MAGICAL compass. At some point, Morgan fights against Spanish Royal Armada and his ship ends up in Davy Jones Locker. Jack later makes a deal with Davy Jones, that includes a life-debt of a 100 souls (or his) for the ship to be risen and rechristened The Black Pearl. So we could assume a couple of things.
- The ship previously had magical properties, as POTC-Wiki sites the Wicked Wench as a "legendary" ship and The Black Pearl as a "ghost" ship, therefor, it may be that Davy Jones (alone) could not ever fully destroy this ship, he can only take it out of commission. Also, why else would Jack want this ship, if it wasn't already special?
- Davy Jones Locker is a magical space where most things are not destroyed, but only if he (or any Dutchman Captain?) is the one to put people and objects in there. The reason I say that is because clearly, the ship used by Barbossa, Elizabeth, and Will (AWE) does not make it, at least not that we know of (it's possible that Davy Jones Locker is vast and we have only seen a small part of it)--but that could have to do with the entry way, more than just that everyone who dies goes to the Locker, as we know most people are "suppose" to get ferried to some "other side". This is a responsibility of any Captain of the Flying Dutchman.
The Black Pearl was an infamous pirate ship, originally named the
Wicked Wench. At one point it was sold and turned into a merchant
vessel before turning back to piracy when it was re-christened. With
sails as dark as a moonless night, and a hull painted to match, this
legendary ship of the seven seas was every inch a pirate vessel. Built
for action, this ghost ship could outsail any other sailing vessels...
The Wench's first captain was Morgan, a pirate who died in a battle
with the Spanish Royal Navy. Command was later given to Jack Sparrow,
who led the Wench and her crew on several voyages from West Africa to
the Caribbean and back for the East India Trading Company on the
behalf of Cutler Beckett. However, after Jack liberated a cargo of
slaves, Beckett ordered the Wench set alight and sunk and her captain
forever branded as a pirate. After failing to rescue the Wench, Jack
made a deal with Davy Jones, the ghostly captain of the Flying
Dutchman. Jones raised the Wicked Wench from the depths, giving Jack
thirteen years as captain, in exchange for one hundred years of
service aboard the Dutchman. http://pirates.wikia.com/wiki/Black_Pearl
At some point in his life Morgan became a captain of a pirate ship
called the Wicked Wench. The Wicked Wench and her crew were part of
the pirate fleet that tried to end Armando Salazar's reign of terror
when the villainous Spanish capitán attempted to clean the seas from
piracy. In a fierce battle off the coast of the mysterious Devil's
Triangle the last pirates in the Caribbean joined forces in an attempt
to sink Salazar's ship, the dreaded Silent Mary, but the mighty
warship and her crew proved to be unstoppable.
Soon, most of the pirate fleet was burning and sinking, and the Wicked
Wench was the only pirate ship left afloat. Mortally wounded when the
broadside from the Silent Mary hit the Wench's quarterdeck, Morgan
gave his compass to Jack, an 18-year old boy, telling him never to
betray it. http://pirates.wikia.com/wiki/Morgan
Some Trivia that may support #1 - The Wicked Wench was already "magical."
In addition some trivia that might be of interest includes the canceled video game, a prequel, Pirates of the Caribbean: Armada of the Damned. The Game featured a new protagonist, Captain James Sterling who gets "cursed" by "Cursed Spanish Ghost Pirates" from a previous era. In the game, Sterling was to "reassemble" a magical wrecked and scattered Pirate Ship called, the Nemesis --AND depending on the choices one would make, Sterling would become a good-looking heroic legendary pirate or he would become feared and dreaded and turn into a ghostly-dark pirate who used a GIANT ANCHOR as a weapon!!
It is unknown who was the original captain of the Nemesis, but some
time after his resurrection, captain Sterling has found the wreck of
the Nemesis on some beach. He decided to save the craft and turn it
into his own pirate ship. Pieces of the Nemesis were scattered all
around the Caribbean, and Sterling spent many months in search of
A LOT of the game's elements seemed to be built back into the franchise, especially Dead Men Tell No Tales with Salazar in particular looking a lot like the "evil" version of Sterling and similar character to the games villain, Admiral Maldonado. The Black Pearl's anchor is featured also, as Carina Smith climbs up it!
A nameless pirate with an anchor on his back, member of the Drifting
Dead, can be seen in Davy Jones' Locker in At World's End (video
In one of the other already-existing POTC video games, there is a GIANT ANCHOR seen in Davy Jones locker--some speculate there would of been a correlation between The Spanish cursed Pirates, Sterling, and Davy Jones, but no one will ever know since the game was never released, only beta-tested, but it's possible that they are taking these ideas and re-contextualizing them back into the newer parts of series with Morgan and his Magic Ship being a kind of equivalent with Sterling and his magic ship and that Jack's Sparrow's story relies on the history of Morgan and his magical objects.