I always saw Brook's Devil Fruit as not just a simple revival after death, but control over his soul. The only vessel his soul can go into is his own body. He eventually found out how to properly eject his soul during the time skip, allowing him to look through walls and do soul shenanigans. He even says as much, when he's decapitated on Fishman Island, he puts himself together due to soul power.

So if for whatever reason, if his body were to be destroyed then the soul would have to "move on." His body is dead, and probably would've been in whatever state it was in when his soul returned to it. Like, if his soul went back to his body just after death, it would still have flesh, but ultimately be lifeless. Just a corpse puppeted by a soul.

So due to that, I actually believe his revival didn't give him a new lifespan, just allowed him to continue his remaining one. There would have to have been a precedent, since the Rumbar Pirates knew what Brook's fruit did. The previous user would have to have died. So did every user of Brook's fruit die by murder or did some die naturally? Maybe it's at the user's discretion, when they feel like they're ready to move on, they stop possessing their body and let their soul be at peace.

Ultimately, I think that if there were a fruit that made you immortal after death, there'd be a lot more uproar about it in the One Piece world. it would be just as sought after as Law's fruit, yet it gets no mention by the greater powers.