I lived in a van full time for over 2 years, I skated, mountain biked, kick boxed among other things and to be honest never even gave a thought to injuries. What was more a day to day concern for me was how sweaty you get during these activities and being able to wash myself as this was not long after covid when I started that life and so gyms with showers n such was not an option.
My opinion of it is that why let the what ifs and this could happens dictate what you do in your life. All those activities have their own dangers associated with them but also the benefits of both fitness and mental well being as well as just pure enjoyment far out weigh the risks in my eyes.
If I got injured then that is something I would deal with as and when it happened. You can negate risk by taking proper precautions and making smart decisions but you could just as easily get hit by a car or something that is out of your control.
So personally I say go for it! I loved being able to wake up next to some trails, have breakfast then go out for a ride. Or wake up next to a beach and go out for a run. I was never thinking about injury. If it happens it happens but don't let the possibility ruin your enjoyment of life! :D