Re: Why not shoot it down ?
In WW1 it was discovered that exhausting a fighter aircraft's ammunition perforating the things simply doesn't cause enough leakage to deflate them before they complete their missions and return home. It was a different story once the fighters started carrying incendiary ammunition, but remember this was still when hydrogen was used to provide lift.
In summary, it would probably be necessary to use missiles, and that starts to become difficult to justify if the missiles cost multiples of the balloons.
WW1 fighters were using light machine guns (~8mm calibre solid metal) with very limited quantities of ammunition. An F22 has 20mm auto-cannons that (I presume) will fire all manner of modern custom high-explosive, shaped, piercing, shredding, incendiary, dousing, gluing, glitter-ball shells in anti-tank, anti-aircraft, and anti Chinese-weather-balloon flavours, and at close enough range the holes should join up into a huge tear anyway. They probably have shells that will take a selfie moments before impact and WhatsApp it to Xi.
It may well be safer and simpler to use missiles however (and target the flight control structures rather than the balloon itself). I doubt the cost will bother them too much. Just putting some F22s in the air is a big expense already, and they'd be in some increased danger of mishap flying close enough to use cannons.
Or the balloon may be above F22 altitude in which case they'll need missile to get the extra height. Maybe China is testing their high-altitude capability? Maybe the Yanks know they're being tested and that's why they don't want to shoot it down? Let's face it the whole 'we might injure someone' excuse it a little fishy coming from an organisation who's entire purpose revolves around injuring people.