It is not that because eggs are too expensive or something, but difficult to transport. The logistic for transporting raw eggs is just hard to archive. You need containers that have enough cushion by light weight, to contain eggs, so that it won't break, and the easy to pack. It is not easy to come by during that time even for the Americans. Considering the main transportation, trucks, were not on the interstate highway, but rugged terrain. Large supply of eggs were just not possible, even for the Americans.