Shooting it down just causes more problems. If we shoot it down we 1) have to clear the potential crash site to prevent harm to residents and 2) figure out what we can do with a giant pile of scrap.
In flight and active, the baloon is more useful to US intelligence sources. What radio frequency/ies it uses to talk back home (if it does), content of the data transmitted, how the gondola is assembled, what's visible in the gondola, etc. We shoot it down and it crashes, we have a giant pile of almost-space junk and no discernable way of telling what it did.
Also, it opens up a whole new ethics question when we go spying in other non-hostile nations with drones, planes, and yes, even balloons (I can't find the link now, but the Pentagon budge last year asked for an increase in their balloon surveillance budget), are those nation's free to shoot our shit out of the sky for funsies? I'm pretty sure the spy community are like Pirates in that they have their own code of ethics they'll follow. And it knowingly goes back decades to where even hostile nations knew the other was spying and kinda-sorta allowed it (to a certain degree).
What is absolutely p*ssing me off about this story are the Meal Team Six / Gravy Seal cosplayers who think they can take their Smith and Wesson M&P15, point it skyward, and think they can shoot down this baloon.
This blimp is floating at 11 miles in the air. An AR15 weapon's effective range is 500 *yards* or 0.28 miles. The baloon is almost 40 times the distance an AR could shoot.