I own only base game and fresh new Austrian expansion, but I have found out, that I use those QRC very rarely. I agree with Mr.Borg, that after figuring out how system works, it is much easier and faster to count/know how much dice each unit has.
And when I play with absolutely new players, I take out QRC only for myself and I keep repeating to them how it works, so they will absorb "counting-system". This would help them to think more about unit and appreciate its value. It is much better then just lazily have *always* a look at QRC at exactly the same thing.
I/we agree/ing with Borg might be minority, but it works for us and the game proceeds much faster. So give it a shot for game or two without these cards. It should be easy for someone, who have played CCN for a longer time (then me).
On the other hand, I understand those, who got used to them. They are addictive and very helpful - for first few games...