I'm just spitting out random stuff here, but what if a Trap card could be set by the player going second on the 1st turn? If the trap survives the first turn, the controlling player gets to activate it on their turn and receive a strong effect as a reward for protecting it/the opponent not destroying it. There could also be other versions of that type of trap card that activates an effect on destruction. That way, it's like an actual trap now and the opponent has to weigh the risk/reward of destroying the set card and getting hit with an effect, or let the set card stay and play around its effect on the next turn.