While I think it makes sense to divide health and strength, it is also true that physical strength and conditioning have a very real impact on health. For example, I have asthma. But if I lift weights and do cardio regularly my asthma all but disappears. So there is a direct link between my physical strength and my health (you have to keep in mind stamina is also a function of how easily your muscles tire and how hard it is for them to perform actions). However I also have serious digestive health issues. No amount of weight lifting or running will improve it.
This.
I've started taking my health seriously, as I have a job that requires a lot of stair climbing and lifting (along with counseling and paperwork). I typically do a LOT of stair climbing, which is a leg workout. On top of that I run at home most days, upwards of 3-4 Km, and a lot of pushups (150 in the morning, plus some at night) and a bunch of weights, squats, etc. I'm physically stronger, which is why my muscles can endure longer.
As well my immune system is getting up there, but some of my reactions and wellness are linked to when the last time I worked out was. yes, there's cardio, but you could argue that even cardio is based on the strength of your heart muscles.
An article I read (the contents of which I can't discuss on this site) talked about other types of endurance that are based on muscle strength. Not how long you can wear yourself (and your muscles) out through strain, but how strong you are.
The problem is that RPGs are about describing an idea, even a cliche, using rules. This is why we have the nerdy, weakling scholar and the moronic jock. Reality shows us that physical health directly impacts cognitive abilitiy (read Brain Rules), as more bloodflow brings more oxygen to the brain and removes more toxins. Not that physically active people are always smarter, but rather that the full potential of a brain is brought out by taking care of it physically: get in 20 minutes of cardio twice a weak, and you reduce the possibility of dimentia as you age.
However, the idea of "balance" and the likelihood that people who sit at tables for hours talking about their awesome character are not in great physical shape, means that we keep the unhealthy mage and the dumb jock, and the strong obese fighter who breathes hard when he walk-runs (tongue lolling, lips blue, gives up chasing the PCs and goes to eat some pie. Mmmm, pie...).
I would argue that the strong obese guy is better able to run a mile than a weak obese guy.
And yeah, Constitution as a score covers a wide range of ideas that work in-game. (For some reason a 3 strength character can run a mile; not a tiny creature that's well built, but any 3 str orc or human.)
But is there a way of making a simulation/game comparison without requiring that stat? That's approximately D&D level simplicity?
How do video games do it? I don't expect that most online or console RPGs have a health stat apart from HP.