Frankly our troops should be spending independence day with their families whenever possible.
And that really is one of the big points. (and a good one from the article). It is what makes the US different. We are not a militaristic nation. It is a necessity, but it is not the center of our nation. Liberty is. We were founded on kicking soldiers off our streets and our army were citizen soldiers doing what is necessary at the time.
Giant military parades like one would see in China, Russia, or North Korea are a sign of a militaristic nation having to show off its might. (some could say over-compensating).
When we do have military parades, they are usually small and celebrate either returning home (fleet week for example), celebrating veterans, or things like small Air Shows which are somewhat of a technological interest for the public- none of these are 'reviews of the troops' for the leader or a reminder of force to the world.
It is a major difference.
I don't think we've had a formal 'review of the troops' parade since Woodrow Wilson and he certainly isn't one I would go back to as an example to follow.