Americans were only in WW2 for about 3.5 years. The Germans had 6 years of WW2, plus all of the fighting from the Spanish Civil War to WW2 to build up kills. Plus the Germans fought outdated planes with the world's best fighters in those early war years, while the U.S. started the war with obsolete fighters going against the best planes & pilots. And finally, American pilots had more stringent requirements to meet before being credited with a kill than the Germans.
All of that being said, the Germans had some of the greatest fighter pilots in history. I've read a few of their autobiographies [such as Erich Hartmann].
There were several reasons for the German kill rates.
(What you mention)
1. They didnt rotate their pilots. A US pilot had a tour so to say.
2. The US entered the war later in reality. The war began in 1939 and we really didnt enter until 1941. We missed 2/5th of the war.
(But there is more)
1. Understand that near ALL of those German aces with these immense kill numbers racked up these scores against the Russians; a force that was flying obsolete planes and had pilots that in part barely could take off and land.
You mention that we started out in the war flying obsolete planes. Well, youre right. The P40 was inferior o a Zero or ME109, but the Russians fly even worse planes! They were flying P39s in part!
2. The Germans were very glorifying and self loving with their reporting on the war in this time. They tended to inflate their success significantly. Actually so did the Russians. If you sit down and to the math, the numbers dont add up. In other words, the Russians claimed to have shot down more planes than the Germans ever built!
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Back in reality mode, what you wrote is spot on. In the beginning he Germans with the ME109 (Their primary fighter through the whole war) was a superior plane. The Germans knew that war was on the horizon and they had prepared over years, actually nearly as soon as Hitler came o power. Events like Legion Condor in Spain helped hone the skill of German pilots and develop doctrine etc. In the beginning they had an advantage. Even the Spitfire was no plane in service at wars beginning.
However, as the US entered the war and began to fully mobilize this advantage in the beginning quickly faded away. Germany as a nation really didnt have a larger nor more capable aviation sector before the war, they had no real skills that were not present in the US, and in fact they had a smaller industrial capacity, lower population, and fewer resources. Once the wheels of war began rolling in the US quickly planes like the P51 began to dominate the skies over Europe. By wars end, neither their pilots, nor their planes were a match. As with the Battle of the Bulge, they even planned their military campaigns around avoiding US airpower by 1944. Once the weather cleared their Luftwaffe took a beating and was no long capable of defending their ground forces despite throwing at us all they had.