Fatigue actually mattered in Oblivion, not at the extent of Morrowind though, where it mattered in nearly everything...
I was always thinking during combat why do I do such small damage at my enemy, and then I realised that my Fatigue is around 0. Also, while you can run fatigued, it won't regenerate fatigue while you're running...
Stamina should be split into two parts, represented on the same bar.
That's... actually a good idea.
Eating, drinking, sleeping should restore stamina, and bad things could happen if exertion reaches the current stamina...