To me, he was never the main character, you can't connect to Jack as a character. You can't get invested in his story, but you can enjoy him. The original trilogy is Will and Elizabeth's story. That is what drives the films, that is what you've invested and connected to. Jack and his story is the crazy world they have found themselves in. They are how the audience connects to the films.
When the fourth film lost them, they weren't replaced and that's why the film didn't work. It was just Jack going on an adventure for no reason, some stuff happens and then he goes on his way again.
The fifth film corrected this issue by having new and returning characters. A story for the audience to connect to. This central aspect could surely exist on its own without Sparrow. As any film works without Jack Sparrow.As plenty of scenes and storylines in the originals worked without Sparrow in them. Might not quite be the same, he might be missed but I don't see why you couldn't tell a good story. You have large than life characters like Davey Jones. You can come up with more if needed.