I actually am very interested in this idea and already considered implementing it (this is commonly called Banish in most roguelikes, so I will refer to it as such).
My primary problem with this mechanics is that game has so many cards (more than 360 currently), that banishing just a few of them will be too small of impact. Game currently has “banishing” items (Porcelain Dove and Anchor) which remove whole classes of cards from rewards, but of course you need to find those items first.
If you have specific suggestions on how to make generic banish more impactful and / or about new banishing items, I am very interested to hear them.