A few months ago I was at the dog park with my wife and dog. My dog and another dog were running around chasing each other when they bowled into an older woman that was standing around in the field. She fell, there was a loud snap, and she started screaming in pain and grabbing her ankle. Likely ankle fracture.
Other than ask her if she was ok - which she obviously was not - I didn't "out" myself nor did I mention that I was a physician. First, I'm a psychiatrist, not an orthopedist. Second, I had essentially zero orthopedics training in medical school, and other than saying, "yup, that's broken, you should go to the ER" there's absolutely nothing that I can offer this woman in that moment that I can't offer as a non-professional bystander. Third, there was a hero "physical therapy guy" who decided he was going to save the day and figure out what was going on. He very likely did know more about fractures than I did. I just didn't see the point.
If I can somehow be useful in a situation then I'm happy to volunteer myself. But as has been said you are not compelled to act, and unless you get some kind of rush from saying, "stand back, I'm a doctor!" I don't see the point if you can't meaningfully provide any care apart from "yeah, you need to go the ER" or, even better, calling 911.