Is there ever a way that a player can use Dampen Light on his opponents turn to slow him down from playing higher cost cards? I guess I'm speaking preemptively here. e.g. It's your opponents operations phase on his first turn. You're holding a Dampen Light and wish to play it causing his 2 cost character to cost 3, BUT the active player ALWAYS takes the first action in every phase leaving me with a useless Dampen Light in my hand that can never do anything. Am I right about this.

Well, you have the mechanism right, but not necessarily the outcome.

Perhaps your opponent is planning on a combo play during the operations phase - he/she plays the first card, you play dampen light, and the combo doesn't happen because the price is too high.

Or, maybe it is your story phase and your opponent has an open domain. You anticipate him/her playing a response card that will mess with your plans (Cats of Uthar? Master of Myths? Power Drain? Binding? who knows - it depends on the deck build). You play your Dampen Light and the plans are thwarted.

OK, Dampen Light is not that great, but it is playable and has a purpose.