James K and Mike Irwin make very good points, I had forgotten about the G41, there isn't much literature about it that I've run across so it rarely comes up in conversation. however I would like to offer my own opinions towards this statement:
Regardless, the outcome of WWII really was not much affected by the small arms used. The Allies did not win because the U.S. had the M1 rifle, or the Russians had the SVT 40. The huge technological advantage the U.S. had in mass production and the advantage the Soviets had in both production and manpower would have made the difference if all the armies had had only bolt action rifles. When a squadron of P.51's descended on a German troop convoy or a supply column with all guns blazing, it didn't matter much whether the Germans had K.98k's or G.43's, they were in deep trouble.
now I will largely agree with you here however there are a couple situations to look at. in the south pacific where much of the fighting was in rain forests and swamps things like P51s, tanks and artillery were largely irrelevant. the heaviest thing you could post were machine guns. had the Japanese adopted a semi auto rifle then the entire south pacific campaign could have ended much differently as the marines were still largely issued 1903s. in this situation the japs had few machineguns and no SMGs while the US had plenty of both, the advantage of firepower(mixed with better supply chains) is what turned the tide in the south pacific, not tanks, planes and big guns.
you are largely correct in the case of the african and european campaigns though large amphibious landings like normandy where you have machine gun fire raining down on you would have been even more catastrophic had everyone been using bolt actions instead of the mix of semi, bolt and full auto weaponry that we hit the beaches with. the rest of the war however were pretty much won but tanks planes and big guns