Why didn't they use machine guns? Perhaps one reason was the risk that if they used machine guns, they would hit the balloon and crash the fighter. In that case, it would have provided China with the worst possible performance of shooting down a U.S. fighter with a Chinese balloon. On the other hand, if they used missiles and shot down the Chinese balloon with flair, we could advertise a strong and brave U.S. The U.S. successfully turned the humiliating situation of a Chinese airspace invasion into an opportunity for the best U.S. performance.
They probably wanted to bring the balloon down as quickly as possible once the decision to do so, and using an exploding warhead makes it easier to keep it in sight as it descended to make recovery easier. Projectile holes would likely just slowly leak for a while making descent take too long.
