If the military had all the necessary information about the previous hijackings and the previous crashings on 9/11 then yes shooting the plane down or at least going after it would have been the best course of action. It was clear that the planes were being used as weapons. It is just a matter of what they knew at the time.
Yes, after Flight 77 drastically changed its flight plan, the military should have brought down the plan to protect Arlington, because it was clear by that point what the flight was going to do. We were unprepared for 9/11, and the military did not react on time to make this happen. But had they brought the flight down it would have saved lives.
If people are aware, as they are now, that planes can do a massive amount of damage, and a plane is in the position to attack key points in important areas, then a military attack can legitimately be undertaken by the government for good measure, and should in real threats.
I do not believe the military should have brought down Flight 77 to protect strategic targets in Arlington after it drastically changed its flight plan. Firstly, there was a plane full of innocent people involved with this hijacking. Secondly, taking the plane down would have still lead to casualties on the ground due to the lack of time.
While it's tempting in hindsight to say yes, consider what we knew about hijacking and domestic terrorism before that day in 2001. The idea that someone would fly a plane into a building like that was not considered. Also, things were happening so fast that it was impossible to put together what was going on until after the fact.