Per guy on Fox, Biden wanted to shoot it down over Montana, DoD and other military advised Biden not to attempt a shoot down. There's a Twitter thread a few pages back that explains why it would have been tricky over land.
The guns on fighter jets use cannon rounds, not bullets. They are designed to explode on impact and the balloon surface wouldn't allow for that, and those rounds would have to come down somewhere. Using a proximity warhead on a missile would have the same issue. It's also flying at a high enough altitude that F-22 would be operating near it's upper limit. Even though it looks like an easy target it actually isn't.
This is one area the new laser pods being developed could really help. It's a shame we couldn't conduct a real-world test yet.