Do you have any figures or stats? I looked, and this was the best I could find: https://www.iii.org/fact-statistic/facts-statistics-mortality-risk

Not sure about your question, but these suggest that dogs are the real problem, although dwarfed by opiods and poisoning.

In general, parks are pretty safe environments (national Forests, too, for that matter). I spent a forty-one year career working, and at times, living in national parks and i was generally safer there than when i was living in town. Of the hazards present, wildlife was fairly far down on the list of concerns.

Next time I'm in serious bear country, I'll carry bear spray.