A military that is actually proud of itself? Yes absolutely its soldiers should be proud of parading.

The issue here isn't the act of parading. The issue here is that the US and its vassal states under nato are an evil empire that do nothing but evil everywhere they go. There is nothing to be proud of, and they certainly do not exist for the people.

When a military that genuinely exists for the benefit of its people parades, its soldiers are proud of doing so, and its people love seeing them do so. When a military that exists for the benefit of its ruling class parades, the parade takes on a different character, it does not look like a display of pride to its people, it looks like an intimidating threat to them instead.

Herein lies the difference between China putting on a parade, or the soviet union in its time, and how that differs to the US. One is a display of actual defenders of the people while the other is a display of enforcers of the bourgeoisie. These have a clearly different character.

So to answer your question "you think the military should happily perform?" No, not the american military. Every single one of its members should throw themselves off a cliff for the monstrosity they're taking part in, or dedicate the rest of their lives to making up for it. They don't want to parade because they know there is nothing to be proud of deep down.