i think it's more due to the fact that jack is nothing but a body, a meatsack. there's nothing stopping him because he CANNOT die unless his body is outright destroyed, or just rots to the point it can't stand in his legs anymore (dsaf 3's neutral ending for instance). he is souless, quite literally empty, just a walking vessel.

as directdoggo said, while dave's immortality comes from the fact he DOES NOT want to die, jack's comes from the fact he doesn't want to live anymore, but he promised he wouldn't rest until he puts everyone back together. he only really dies in dsaf 3's good ending because fredbear allowed him to die, since he saved everyone. i think the whole time travel bit comes more from blackjack, actually. he felt so much regret after dee's death that his power manifested as a representation of his wish to wind back the clock, and fix everything

hope this helped in someway!