On that basis you'd also have to exclude coverage for injuries from almost any sport or exercise activities done "by choice"

It goes way further than that. How about people who have children (again a choice) as that also increases health expenses. Living in areas with more sun (let's call that a choice too) means more likelihood of skin cancer. Those people using private cars rather than public transport are also more likely to be more severely hurt in more accidents. Someone engaging in "bad behaviour" like smoking may have higher health costs at the end of their life, but their lifetime total costs may be lower because their life ends quicker than healthy people having a longer end of life period. (And the smokers paid more tax, collected less social security etc.)

Realistically all legal choices and activities have to be covered, or you would be arbitrarily victimising certain groups.

The personal responsibility riff gets really problematic when you are faced with things like alcoholism or venereal diseases. People certainly have a choice to keep alcohol consumption down practice safe sex &c. But it's a reality that some people catch STDs or drink too much even though they should not, and these things have a way of affecting more than the afflicted individual.

And food deserts are a very real thing. If you live in one of those you haven't even much of a choice regarding obesity.