The military is worried about the consequences of debris hitting something on the ground. Wherever it winds up, it will make a mess. Sending over a balloon like that was a hairbrained stunt by the Chinese. Overreacting will play into their hands.
My guess is that the “military” recommended not shooting the balloon down because it can’t.
The altitude is beyond shooting down capabilities
If they’d taken it out over the Aleutians, the chances of it hitting someone or anything of significance were very small.
What’s the point of having NORAD or military bases in Alaska if they’re going to be afraid to shoot something down?