Don't know, but I would think much more Army casualties than Army Air Force as the grunts moved across Europe. Then you have Marines in some of the bloodiest and fierce fighting in the Pacific. I'm just guessing. Sure there are some WWII historians who would know. Bottom line: All the services lost good men in horrendous ways because of the totalitarian Axis.
What has always pissed me off is that we not only gave their nations back to them, but helped rebuild. We should own all 3 nations. Think about that.
I definitely get your point. We could be a modern version of the British Empire, perhaps the subdued world would be more peaceful, but it might be much, much worse. For thousands of years might made right and borders ebbed and flowed based on how much power a state could project.
On the other hand, there is something to be terribly proud of considering we could quite easily control much of the globe, but after conquering, we just bury our fallen and rebuild. Yes, we had a pseudo-empire phase and the Indian Wars weren’t our best moment, but a nation that uses our military and naval forces for the benefit of others is pretty new to humans.