Arguments around force projection are certainly going to be popular inside the beltway. At a certain point the deficit does become a national security concern, and announcing to our adversaries that they can exacerbate that timeline with incredibly inexpensive balloons is no longer "projecting" anything that resembles "power"

Jingoism isn't power.

My brother in Uncle Sam, we’re only one week into this “crisis”, which is widely overinflated. China is posturing about balloons in its own South China Sea, while America is gassed up about balloons over the Alaskan heartland. This is the posturing phase, and a missile or three is a rounding error in the US defense budget. I don’t see the economy losing buoyancy yet.

Nevermind that the training value of firing a live AIM-9X at a live but odd target is probably worth more than $400k on it's own.

Bullets (20 mm cannon shells) could work to an extent. But they are short ranged and require the fighter aircraft to get close to the target at a high closure rate. This creates some risk of a mid-air collision. Using guided missiles is much safer.

Canon rounds aren't great for balloon targets. It's quite likely that a balloon doesn't offer enough resistance to trigger the fuzes, which leaves you with a bunch of live rounds falling ~40k feet and hitting whatever is below. While self-destructing rounds do exist for the M61 20mm canon, they aren't cleared for aircraft use, only for ground-based use.