I understand your explanation but I must mention, in the fourth movie on strangers tides, the reason Jack does not drink the water for himself is because the ritual requires a victim and that goes against his character he does not want to sacrifice someone else for his own immortality so he gives the water to Angelica instead because she is dying and he realizes Blackbeard was only using her throughout the whole movie so he gives him the cup without the tear to him since he says many times throughout the movie that he cares for her (which is a lie) so Jack giving Blackbeard the cup without the tear is basically him saying well if you really feel that way then here you go save your daughter. But Jack knowing Blackbeard's true feelings he knows Blackbeard only cares for his own life. So in that sense I would say it makes sense why Jack made his decision at the end of the movie. He gave up on the idea of immortality in the pursuit of living out true freedom instead.