Throughout the first three films, Captain Jack Sparrow's character arc focused significantly on his search for immortality — perhaps for too long. Jack Sparrow was the kind of character that wanted to be virtually untouchable — the best pirate there had ever been. However, time and time again, Sparrow learned that the cost of immortality far outweighed the benefits. He seemed to come to this realization at the end of , but the plots of subsequent films entirely wasted that progress.
When Jack Sparrow was introduced in he was working on getting his ship back from Captain Hector Barbossa, who had mutinied to chase after the of the Aztec Treasure of Cortés. Jack himself had been the one to discover the gold's location, and he had heard the rumors that it was cursed to make a man immortal. He was eager to seek it out, but he was betrayed. Of course, this wouldn't be the last time Jack Sparrow faced negative consequences as a result of seeking magical items that could give him eternal life.
The first three movies saw the rise and fall of Jack Sparrow's immortality arc. After he was left to die by his crew in , he made it his mission to get his ship back. When he did, Sparrow came face to face with the reality that the Aztec gold truly did hold a curse. Still, when it came to the moments before the curse was broken by Will Turner's blood, when he stole a piece of gold from Cortés' chest. He had wanted to experience immortality just for a moment, even though he knew it wasn't a long-term option.
Leaving the Isla de Muerta and the cursed gold behind, Jack Sparrow had to find a new prospect for immortality. This came in when he discovered the secret to Davy Jones' existence. Once again, this came at a cost. The person who stabbed the heart of Davy Jones would become the captain of the Flying Dutchman and be tasked with ferrying the souls of those who had died at sea to the afterlife. While considering this possibility, Jack wound up confronting death himself when consumed him.
When Jack Sparrow returned from death in , he was left with a lot to think about regarding immortality and the cost of taking on Davy Jones' curse. This was the most significant internal conflict he faced in the series, bringing together all the aspects of his character and ambition. This came to a head in the Battle of Calypso's Maelstrom, when Jack gave up his opportunity for power and immortality when he used Will Turner's hand to stab Jones' heart, thus making the boy the new captain of the Flying Dutchman.
Jack Sparrow's decision in went against everything he had claimed about himself. He sacrificed his ambition to save . This demonstrated his moral growth, but it also revealed Jack's conclusion that immortality came at too high a cost. This was undoubtedly true for Will, who, while alive, had to be separated from Elizabeth Swan for a decade at a time. For Jack, it would have meant a limit on his freedom, which, at the end of the day, he wasn't willing to sacrifice.
Between dying in and coming back to witness the costs of messing with the supernatural in , Jack had learned that the kind of power that he believed would make him untouchable was never what it seemed. The terms always came at the cost of freedom, love, or sometimes both. It was the satisfying resolution to Jack Sparrow's character arc. However, the very showed Jack pulling out a map to the Fountain of Youth — which essentially threw this arc out the window for the sake of continuing his adventures.
Though the franchise could have ended beautifully with , picked up the Fountain of Youth quest that the former had suggested. Once again, Jack Sparrow and Captain Barbosa (not to mention Black Beard) were competing to reach a magical item that would grant them immortality. This could have contributed to Jack's character arc by teaching him a new lesson, but the Fountain only demonstrated again that power comes with a price. To gain eternal youth, the Fountain had to steal life from another.
Once again, walked away from another immortality-granting opportunity, because he was ultimately unwilling to pay the high price. The well-rounded, satisfying conclusion to his character arc in was deemed redundant and without direction. While several factors have contributed to the poor performance of the movies after the initial three, it can be summed up by this kind of arc disruption and stale repetition. Just like the post-credit scene in , which hinted at a Davy Jones' return, the Fountain of Youth plot line felt like a strenuous effort to keep a story going that should have ended with previous installments.