I much prefer to buy full cases. Twelve bottles of wine is always better than six.
They look nice but often times affect the functionality. They tend to restrict access to the battery access or memory card slot. But the same would be true for film cameras. To change a roll, you have to remove the case.Half cases are 10% off every day at our local Kroger store, so yes, I do use them fairly often.
My apologies for a flippant answer, but I have never heard of a "half case" in a photography context.