I am convinced the reason that Premonition was included in the Chapter 2 Core Set is because the designers intended for it to be used with Will of the Cosmos as a way to easily discard Doom that gets added to a player card from Will of the Cosmos under a player's control.
When Premonition is played, it is under a players control. Under the rule Ownership and Control. "Cards by default enter play under their owner's control. Some abilities may cause cards to change control during a game."
Will of the Cosmos adds doom to a player card. arkhamdb.com