Keep in mind that the first four digits are highly predictable (they indicate the type of card and a few other things), and some of the other digits are check digits, so obscuring those provides little additional security.
As thightower's postscript suggests, feelings count for something, and oughtn't be lightly dismissed.
If I could add one card type to the pick list it would be Store Card. Lots of us have store cards in our wallets.
If I could add a second card type to the pick list it would be ATM Card. I would use it to record PINs and customer service phone numbers for bank account and brokerage account cards that I rarely if ever use for making purchases.