"Europe has its soldiers in active missions in Iraq, Afghanistan, the Balkans and many other places on this world. If European courts would prosecute American soldiers (no matter if this would be justified or not), it is very likely that US courts would prosecute European soldiers in return."
1) Soldiers from European countries would first have to be charged with a crime.
2) USA has no jurisdiction in the balkans.
No problem. What about the sexual harassment, the bordellos and the corruption??! I.e. the oil for food scandal is absolutely no issue in Europe but it would be one if the US would arrest a European politician for it. The world is bad. No matter if it is in America, Asia or Europe. You will always find something justiciable
2) USA has no jurisdiction in the balkans.
US courts declare themselves in charge of every BS on this earth. I.e. the nazi implications of Swiss banks. Why should they not cover war crimes of soldiers from Europe??!
P.S. It is good to see that you pointed out the systematic legal difficulties of such action. This is the best proof that America is a good democracy.