Big bucks are an indicator of habitat health.
I don't know what the definition of "herd health" is. The most logical definition you could give is a population's ability to replace itself, ie reproduction. A good measure of reproduction is the body condition of the females, does. Better body condition of does = healthier fawns and thus better survival rates into adulthood. As a sidebar, big bucks are produced by does in fantastic body condition and there is plenty of research that gives evidence to that. So, what produces healthy does? Is it limiting seasons and not shooting bucks until they are 6 yrs old? Is it limiting doe harvest? Some other management strategy? None of those. Healthy, high body condition does are produced by good to great habitat. So, by that logic, big bucks are indicators of habitat, particularly really good or great habitat.
Now, age has something to do with it and our management style in MT certainly affects age class. But, we get plenty of old bucks that are in no way "big".
Research in both whitetail and mule deer is showing that habitat affects both the resource partitioning to grow large antlers and changes the way genes are expressed for large antlers. In other words, habitat quality increases antler size concurrently and into the future. Good female condition (a surrogate for habitat conditions) can change the genetic expression for antler size of her offspring in a single generation. Stacking years concurrently of good/great female body condition (and thus good/great habitat) over time produces more big antlered deer. "Good genes" = habitat.