While yes, there's no certainty that Jones dies, I think it was probably felt you didn't need to define it because of him flopping over the side of the Dutchman like a rag doll.
In the POTC universe, magic is abound and you can easily write some spell or whatever to bring him back.
I don't know why, but I don't feel like bringing Jones back in a post AWE film would be good, I just feel like his character would be in circumstances where he wouldn't quite be the Jones we enjoyed in 2 and 3. While Barbossa served good in 3, he was pretty much the same Barbossa we came to like in the first film.
I would love to see them do a prequel of the original Sparrow-Jones deal, then Davy would be the same, and we'd see an interesting story unfold as well.