The main reason is that too many private sellers, even when given explicit instructions to do so, don't include
a)their name and address with the gun, so that the dealer can log it in
b) the name and contact information of the person who bought the gun, so that the dealer can contact them and let them know their gun has arrived.
Most FFLs include a copy of their license with the gun, as well as an itemized receipt which lists the purchaser. Many private sellers include a copy of their driver license and a note saying who the gun belongs to. These are great.
I've gotten packages that contain only a gun, no paperwork at all. Every once in a while someone uses their work shipping dept. to send a gun with no paperwork, so then I don't even have a return address.
If every shipper included the information they were supposed to, more dealers would probably accept shipments from private individuals, but I find that dealers are much more likely to include the needed information than non dealers.