Another issue to consider is that the BandAid-style bandages (
NexCare are my favorite and are available cheaply at Wal-Mart) are very good for what is truly the most common & potentially serious injury: nicks & scrapes to the fingers & knuckles. FAKs are not just about blood loss.
As Doug Ritter explains, it's common and easy to get little dings on your fingers that then get dirty and infected. A few NexCares and some Neosporin will be very useful a lot more often than 4x4s. Think about this too: using a chunk of 4x4 on a skinned knuckle 1) uses up your tool for real blood loss and 2) results in a bulky bandage that will almost certainly NOT hold up as well as a good waterproof NexCare.
Your hands are vital tools in any crisis situation; you don't want them getting infected and you don't want bulky bandages sloughing off of them. This is a major reason why I keep a pair of thin, good-fitting goatskin gloves in my EDC bag. How will having a chunk of 4x4 taped to your finger affect the fit of your gloves? NexCares are effective while being slim and non-bulky.
Since there is practically no downside (in either bulk, weight, or cost) to having some NexCares in the kit, I don't see why anyone would eliminate them.