If you're broadcasting at higher powers (to send over longer distances) there are risks from high RF exposure and electrical hazards. The HAM radio license exams focus on these safety issues quite a bit.
Sounds like you have never had an RF burn before. The sensation is a lot like a sunburn, but is hard to get if you are electrically close to the ground. Higher frequencies can still give you RF burns when you're standing on the ground.
RF exposure on the ground from an aerial are likely non-harmful. Right next to the antenna can still give burns. There's also issues of arcing, lightning, and other electrical issues when dealing with high power radios.
Electricity is unforgiving and a lot of the safety rules in licenses above Technician try to instill that fact.
Lots of people hurt themselves when falling off a ladder trying to put up an antenna.
Joking aside, there is a minor risk of RF burn if you do really stupid things that you have to learn not to do to get a license. I can’t really imagine someone getting hurt by the radios themselves.
You can also easily cause interference, which might not be directly dangerous, but can certainly be problematic if you're causing problems on important communication channels.
