Yeah, picked up cards stay in your deck for the whole arena and replace the card that was in slot, although it's not clear enough.
What do you think about that?
I think it's fine, but it makes your starting cards less important, and makes getting good drops (not so much what cards appear but what card you are allowed to swap out on a given turn) really important. It also rewards playing a single level as long as possible rather than opting for a quick victory. This means, for example, that healing abilities are somewhat more valuable in the early game since they help you drag out an easy fight while you wait for the cards you want to spawn.