Even if it is possible, is it secured enough?
I don't know how private key will be protected if we include it in our signature when signing a transaction on radio waves. It sounds a very old technology for army forces centuries ago. Do we really need to do backwards technology after we already have the Internet and Blockchain technology?
Security is most importance so if by any mean, radio waves can be a secured channel broadcast Bitcoin transactions, I won't be against it.
Without thinking about it too much, there shouldn't be too much of a difference to how you send them through the internet now. So, the question of security should theoretically be the equivalent. Its just times have moved on mostly from radios i.e for your average person, therefore its the issue about practicability, and convenience rather than security.
It is very important to remember that when you are considering a method of communication, the hardware that method requires has to be easily available at home and majority of people have to already possess that hardware. For example when bitcoin is used over the internet, majority of people already own a PC or a smart phone to communicate over the internet, so it is the perfect way. But if radio waves, satelite, etc. were to be used then majority of people won't have the equipment already and setting it up would take a lot of effort for them, so it is not favorable.
Exactly, radios are slowly descending into extinction for your average person. Mainly only used at certain organizations, emergency services, and hobbyists now. Setting up a
local internet even if the government was looking to restrict it would probably be easier because of this reason. At least, if you wanted to be able to send to the most people possible.