I feel like Wind Waker was that middle ground. You didnt have to explore the whole overworld map but you were rewarded for doing so. It also still those progression based dungeons.

It literally does tell you if you own the card though. It also tells you how many copies of said card you own. Have you ever tried to craft a card in game? When you click on a card there's a space that says owned: along with how many copies you have.