I think healthcare can be more of a "do as I say, not as I do" situation. They can be perfectly knowledgable, even if they don't follow their own advice. Life isn't as easy as "just do it", and it's likely helpful for many people to work with someone who understands that.
And if we don't just cherry pick one thing and instead look at the litany of health issues that may be self-inflicted in medical professions, we probably wouldn't be left with many doctors/nurses.
You would've had me at military, law enforcement, fire, and EMS...but healthcare? That industry is already fucked and you want to send it back to the dark ages because, they're not in shape?
Everyone has there own version of obesity going on, but for some it's their weight.
I think it's something along the same vein as an overweight fitness instructor. I think it's an innate requisite that if someone is presenting as a professional, that has instructions for us to follow, that they at least have the appearance of following their own guidelines.