Why then would one use these cards as a regular close combat attack gives a higher attack value?
Two main reasons:
1) Some units (like LMGs, HMGs) have a negative CC modifier. Having no CC modifier is better than a negative one.
2) The card doesn't use APs or CAPs, so if your unit is spent and you have no CAPs left, you still have a last ditch way of defending yourself.
Also, you can use the cards to group fire - i.e., add +1 to a regular CC attack.
The only thiong we could come up with is that the CARD doesn't give a CC modifier, but the unit does so you're supposed to add the firepower of the card to the firepower of the unit with a CC bonus. Is this correct?
No, this is incorrect.