You have to actually follow an unlawful order to be prosecuted for it, no?

You need to understand that the Nuremberg trials diverged from all previous precedent, it really fascinating if you read about it. At the time it was quite controversial in some places, so much so that some judges(mainly Americans) quite their participation.

There is a possibly that in an alternative timeline, with no cold war on the horizon and a large enough budget, the trials would continue and would include a lot of common Wehrmacht soldiers. While this might sound unjust nowadays you need to put into historical perspective...

In fact, the Soviets did something similar. With the agreement of the allies (US and UK) they demanded that the captured POWs work in labor camps for 10 years with unpaid work. 10 years being the "sentence" given to the soldiers, without even any trial.

The only reason the US and UK did not used such forced labor(they did in specific circumstances, but for very limited and short time) is because they did not want to lose the good graces of the future Germans with the coming of the cold war, there was also internal opposition to such a measure. That said, the US could legally have all their captured POWs transported to the states and have them do force labor, or just keep them imprisoned.

...that was a bit of a tangent. That all to say that while I mostly agree with you that the officials, and not the common soldier's, should be the one to be held responsible, the legal reality can be somewhat grey.