Would the world be in a worsen state without him?
Let see, Crocodile will be king of Alabasta and be warring with the World Government. Smoker would have stay in Easy Blue and stop Arlong from taking over. Buggy will still be small time and probably get caught by Smoker. Coby will still be a pirate and Alvida won't have devil fruit powers. Iceburg would die and Water 7 won't be the same. Gekko Moriah would still be a Seven War Lord. Enel would kill everyone on Skypiea and go to the Moon easily. Caesar Clown would kill those kids, because Law don't care. Hody Jones would destroy Fishman Island and kill Shirahoshi and King Neptune, but die when he try to fight the World Government.
Would Ace still be alive or even captured for that matter?
Ace might try to become King of pirates in honor of Luffy, so he wouldn't join Whitebeard. But the World Government will catch him and kill him and no one would save him
Heck where would the Straw Hat Pirates be?
Zoro would have kill Morgan and Helmeppo and he would still be in East Blue
Nami would lose all hope and be send to Jail by Smoker for working with Arlong
Usopp and everyone on the Syrup island and Kuro's crew (beside Kuro) would die.
Sanji would destroy Don Krieg and still be a cook on that boat.
Chopper would have been eaten by Wapol.
Robin would still be on the run.
Franky probably will be send to Impel Down.
Brook will still be on that ghost ship with his death friends
Would Some of the Straw Hats live until where the time of the manga is now?
Zoro, Sanji, Robin and Brook would still be alive. But the rest are most likely dead.
Would some of them even end up being evil in a world with no Luffy?
Boa will still be the same, Ace will be dead, Law will careless and probably be under Doffy's control (or die)
The One Piece world will still be the same overall, but the islands the Straw Hat visit will be worst off