I have no doubt that patients are getting exposed to more radiation via imaging than they need to.
However, every decision in medicine is (or should be) a risk-vs-benefit analysis. Cancer is not the only thing you can die from. If you suffer a head injury and end up in the ER and get a CT scan, you may increase your long-term risk of cancer, but you are also drastically reducing the risk of dying from a brain hemorrhage that couldn't be identified by any other method.
However, every decision in medicine is (or should be) a risk-vs-benefit analysis. Cancer is not the only thing you can die from. If you suffer a head injury and end up in the ER and get a CT scan, you may increase your long-term risk of cancer, but you are also drastically reducing the risk of dying from a brain hemorrhage that couldn't be identified by any other method.