The FAA defines what does and does not need a transponder, vehicles under a certain weight, under or overflying commercial airspace, or are unpowered (like manned hot air balloons) do not. Hobbyist balloons are both under-weight AND overfly commercial airspace, so don't need one on at least two grounds.
Plus a transponder, battery pack (that works at those temperatures), and sensors, would likely cost in the excess of $1500~ and weigh more than the hobby balloon as a whole by a lot. A radar reflector isn't really required with a balloon because the entire side of the balloon itself is a radar reflector.
As to why the US used a $400K missile to shoot down a balloon? I'd argue they used a $400K missile to avert political criticism, since the media decided to turn it into a thing.
The reality is that signal intelligence can be gathered on the ground and sent back to China trivially. The US isn't a police state after all, gathering signal intelligence is passive, and shipping it back to China isn't a particularly hard problem. We already know that almost all embassies (including "friendly" ones) do so, and it is likely China has some satellite capability in that area too.
