All of the card ownership and battle history is openly available information on the blockchain.
IMO a better solution is to make that information more available rather than dumbing it down. There is already an alpha free to use app that is doing this. https://risitasapp.splinter.monster
I agree with you that bots should not have any advantages over normal players, but I think enabling normal players with better tools/information is the best path to take.
So instead of your idea, "Any time information confers a competitive advantage on bots, we should obscure it wherever possible."
I propose "Any time information confers a competitive advantage on bots, we should make that info available to normal players wherever possible."