Warlord beats Troll, Troll beats Elf, Elf beats Water Sprite, and basically everything else beats Enchanted Bunny.
It says, you may destroy a construct. For the vast majority of things in Ascension, a = one time action.
Consider how (even more) powerful Arbiter of the Precipice would be if you could ignore the banish a card limitation and trash as many cards as you liked.
I argue about this all the time with my wife. I agree with you: a = one time action.