We do irradiate various foods, have been doing it for many years. The commenters who immediately started ranting about "how stupid we are" didn't seem to check first. I first learned that we did it with strawberries and a few other things many years ago (in the 90's maybe), but never bothered to looked up exactly what all foods we irradiate. So I don't know about alfalfa sprouts, but I suppose there are probably reasons why it's done with some things and not others, such as which ones it's safer and/or more effective on, and how it affects the quality of different foods.
The FDA first approved the use of irradiation in 1963 to kill pests in wheat and flour. To date, the FDA and the USDA have approved food irradiation for use on fruits, vegetables, spices, raw poultry, and red meats. https://www.fsis.usda.gov/food-safety/safe-food-handling-and-preparation/food-safety-basics/irradiation-and-food-safety-faq
