I received a cortisone shot in m elbow back in ~2016 for tendonitis. When I did my Separation and Retirement Physical in 2019 for my retirement from the Air Force, a medicine physician administered it and reviewed my records. He would've never done a cortisone shot in my elbow for the reasons that you mention for the chance of it tearing or popping.
I can promise you that players jn the NFL have the same treatment from their medical staff and it certainly will weaken tendons to the point of a single hit causing complete tendon avulsion.