You don't actually get 2 pieces of information as it's essentially a d52. You can process the information slightly faster, but then just roll a d4 and a d12 simultaneously.

Cards are only self-correcting if each player has their own deck. If the bad guys draw 3 great cards, that means the good guys are much more likely to end up with bad cards. You can also count cards, so make sure that's a intended feature and not a bug.

I'm not sure what you mean by a tangible resource for other mechanics. Do you mean you can draw into your hand and use later? If so, that's one of the great advantages of cards. If you just mean you can save the result, you can do the same thing by just setting aside dice.

I takes longer to draw a card than roll die. That's really adds up over the course of an evening and is much longer than the one time someone rolls a die off the table. You also need to shuffle cards, which is a PITA.