Actually, the Ordnance people were told to develop a lighter weight, lower recoil cartridge with better feeding and (in automatic and self-loading weapons) more reliable extraction, i.e. an assault rifle cartridge. They developed the T65 which has less body taper (making feeding worse); and a shorter case, which helps to reduce frequency of case head separation in machine guns. The reduced body taper also makes extraction harder with over-pressure loads (this issue being more pertinent to hand-loads than service ammunition).
The FN FAL and G3 were actually developed as assault rifles but could not be used as such, due to the excessive energy of the T65/.308 Winchester/7.62x51 NATO. The earlier introduction of the new round by Winchester meant that the company could advertise all that nonsense about easier feeding whereas the colonels and generals could not! It is my understanding that 1 million U.S. Dollars was misappropriated for Garand development before WWII, with multiple weapons bearing the same serial number for the initial trials. A second scandal could not have been ignored.
N.B. Anyone who says that the T65 was needed for belt-fed machine guns misses the point! Belt-fed ammo comes in different tins and the Swedes were way ahead of everyone else because after WWI they developed a special 8mm machine gun round inspired by the 8x64 Brenneke (developed for the German Army in 1912).
In fact, I suspect that one of the main reasons for the U.S. push to adopt the T65 was that the German sS (heavy bullet) 7.92x57IS load (introduced in late WWI) was likely to take over the belt-fed role for support weapons in Europe. It is superior to all .30-06 machine gun loads. It was adopted by the British Armoured Corps before WWII, was standard for the WWII German forces, and other countries; and was used in the German tanks taken into service by other countries after WWII. It was also used in the new Panther tanks built for the French after the war, not to mention the LT38-based Hetzer Tank Destroyer that the Czechs continued building postwar.