But the point isn't that e.g. walking fast is bad for your health, it's that when it isn't being explicitly trained for, it is a marker of health. Once you explicitly train it, then it stops being that marker, even though it may still have positive effects on your health.

What we need, in order to understand these proxies, is an understanding of the mechanism by which they work. Take this example: Suppose I am a smoker. I notice that I walk very slowly because I have bad cardio vascular health. I hear in the paper that walking slowing is a marker for death. So I train walking fast. I get up to 'elite non-athlete'. Even though I'm still smoking. In this case, even though I've successfully improved my health, as an indicator, my walking speed will over-predict my health.

For grip strength it's even easier, since it seems very unlikely that actually have a strong grip is realistically correlated with anything health related. Rather, have significant untrained strength is probably very well correlated with a host of genetic, enviromental, and hormonal factors that would likely be strong predictors of health.