J.N.
I get the X-rays for my kids. It's the only way to monitor what is going on below the jaw line (with the incoming teeth), and it can catch some cavities much early than just the oral exam - sometimes early enough that they don't need to drill, just fill (that's happened to me a couple of times).
They take plenty of precautions - the kids get to wear those fashionable lead aprons (lol) and the radiation for modern X-rays is really not a huge amount, less than it used to be iirc. I believe that the benefits outweigh any risks.