I guess it’s because dogs are only carrying their own weight, we’re not medicating them in order to keep them working ie carry us. (fwiw, I wouldn’t inject a horses joints either. I’ve had steroid injections into my knees and the pain is phenomenal and no long term improvement).
Have seen it done a couple of times in practice but it doesn't seem to have a more noticeable effect over other drugs. Also dogs need to be under sedation or GA which is a big cost for most dog owners. Also agree with rara007, most of the time it's done in horses for performance reasons.