Both kids and radioactive material need supervision. Like a child, an energetic radioactive molecule will become less energetic as it ages. Certain materials, like those used in radioactive medicines, have only low-level radioactivity and will decay in only a few days or months.
After all, for the basic body plan to change, not only do you need a random genetic mutation that results in a sixth finger, but that mutation must also provide an evolutionary advantage when it comes to reproduction.