Losing stamina when you miss makes sense, but why not when you hit? If a caster flings a fireball and the enemy moves before it hits, the mana has gone to waste. Also it doesn't make much sense that you'd get tired swinging an axe through air, but not through flesh. I agree there should be an impediment to just slashing through everything and anything though, but just like a caster, even if every hit connects, you'd have to rest for a moment eventually to recover.
I'm not sure how blizzard is balancing health potions against the red-orbs that drop, but they may become the primary source of recovery, though leech will probably be back (seems like a franchise staple at this point; D1's Undead Crown anyone?

). I think rewarding players who use fewer recovery items would skew toward more ranged-attack and caster classes, who simply get hit less often. An interesting idea though, rewarding skilled play is always a plus!