Though this has problems just like anything else.character => situation => setting
The big one: the player does not take the bait.
So the GM takes the time to use all the character stuff about how they are part of a family of god killing group of cool assassins. The GM sets up a nice situation hook "oh no three of them super assassins were killed by hands unknown at a bar."
The GM hopes that by using the players own personal creation that they play might not only pay attention during the game, but be actively motivated to engage and immerse themselves in the game
But plenty of players won't care. They will just say "cool story GM" and then have their character hide outside the bar looking for a target to attack.
Almost as big: the endless argument.
The GM says "the assassin family did this action" and the player jumps up to scream "no way". The player disagrees with the reality of what the GM is doing and demands it be changed to their viewpoint. "Just one family assassain can kill a god, so there is no way three of them could ever be killed in a tavern GM. Your using my lore incorrectly!"
This is just like the play problems if the GM makes the setting first. So nothing much changes.