Unless you just want to spam weaker attacks, a high stamina is a must for any melee centered character. Power attacks break through blocks, stagger opponents, and benefit from perks that upgrade them to make them even deadlier. Not to mention that power attacks kill enemies faster, which shouldn't be overlooked when you're fighting more than one enemy at once, which is pretty often - haha dead enemies can't hurt you - when you're faced against a 3v1, being able to kill 2 of them quickly can give you a huge advantage.. Additionally, for the sword and board types, a high stamina lets you use your shield as an offensive tool and is great for keeping the enemy off balance. A staggered enemy = dead enemy.
Carrying capacity is a nice little bonus, but for any warrior build, high stamina means a deadlier warrior.
I see what you're saying with the restoration perk that replenishes health as well as magic, but if you're too low on health you're more likely to die in just a couple hits where you're not likely to have time to heal. And with low stamina, you won't be as effective with your weapons if you keep having to break away from combat to bring your stamina back before going back in.
For my mage I've been doing 5 in magic, 1 in health every 6 levels. And for my assassin and warrior I've been doing 3 in stamina, 1 in health every 4 levels. It's been working pretty well. I've found it hard to spend upgrades into magic, health, and stamina without ending up spread too thin...so if you're a magic user you may have no use for stamina.