Yes the military honors soldiers, but most of the welcome home crowds you see honoring the troops are their family and friends. I think the point of the parades is for civilians to welcome them home and offer some sort of thanks from a greatful nation. Most civilians couldn’t care less about the military, and that includes many that consider themselves to be conservative.
I think that wars since WWII were not popular, no clear victory or America’s enemies vanquished like in War2. Most welcome Home, Thanks For Your Service parades are done on Veteran’s Day.