Like when people start running and they have all these wonderful side effects 
  — more energy, better sleep, mood improvements

I can definitely vouch for that but I would not generalize it by saying everyone will feel the same way. The changes in me are remarkably stark when I do exercise/jog as compared to when I don't at all. I would like to counter the possible argument that I go for an exercise when I'm in better mood or feeling high energy by stating that I've had the mis/fortune of trying it out during various states of my being.

I think there may be an evolutionary aspect to it as we started of as nomads and the lifestyle that we live currently is the result of the industrial revolution and hence quite recent.