One with more fatigue can sprint farther able to catching up to the one who has less... and that if we assume that there are no sprint perks, that change the speed of your sprinting.
I would even argue, that unless you raised your speed deliberately, it still mattered more on your armor...
Where would sprint speed be increased? What skill would it make sense to be under?
Listen, sprinting longer ≠ moving faster. It certainly does not mean sprinting faster. I think a much better solution would be this:
Race has a minor modifier to base speed. A Bosmer will move faster than a Dunmer will move faster than a Nord. Now on top of that you have Stamina increase your base speed as well as your encumbrance. Then we factor in armor. Armor will not be a straight modifier, either. Heavier armor causes diminishing returns on Stamina at a mildly exponential rate, such that if you're wearing Daedric armor you will be much slower than if you were wearing Steel armor, even if the Daedric weighs less than twice as much as the Steel. Lighter armors will help you to move dramatically faster than a heavily-armored juggernaut, and if you're playing a sneaky character whose only armor is the shadows he hides in, then you'll be rewarded with some lightning-fast movement speed. And there we go. Equipment still plays an important role but you are directly rewarded for choosing Stamina over Health or Magicka. Simple, effective character variety that is perfectly in line with the philosophy of the new character system. High-level perks can decrease the armor penalty while still not letting you move as fast as an unarmored character. Everyone's happy. Well, I am at least, and that's what really matters.
Hmm... I think I might be on to something here. Maybe there's some modding in my future.