It seems like this sort of implementation absolutely requires the client making certain predictions and assumptions. Which just trades accuracy for apparent ping.
For your fight with a mob to be "lag free" the game has to assume that, say, none of the players throw a fireball at your mob. If one of them does, then it has to retroactively correct for a mistaken assumption. That makes for weird inconsistencies and rubber-banding. Which can be just as aggravating as playing a game that runs at the ping of the slowest player.