There was absolutely no reason for Captain Barbossa to sacrifice himself and die. He could have simply kicked Captain Salazar on top of the head as he was climbing up and then spent the rest of his days with his daughter. Instead Hollywood feels the need that every film needs a hero who sacrifices himself.
shareWell perhaps he did not.
He lives by the code of treasure hunting and would die for a treasure at any time. This he stated earlier. He realizes then and there that his daughter is his ultimate treasure. This he more or less says. So to protect her he would sacrifice himself. Logic works.
Question is then IF it was necessary here? Perhaps not. He makes a bold pirate like jump to save his treasure and here he could luckily again have caught the chain and stayed alive or he could unluckily not... he did not.
Was it a sacrifice? No, it was a risk he gladly took because this was a pirates life... in short I say, he did not outright sacrifice himself, he died doing what it is he does best. Being a pirate hunting for treasure.
And besides, it is not the first time he died, so perhaps not his last either dot dot dot