Brother MacLaren said:
Of course you won't need it, but some players will still want it. Increasing base class power just won't do it. Look at it from the character's point of view. No matter how much power a PC has, as long as there is a real chance of them losing a fight now and then they will want MORE POWER. And why shouldn't they? This is their life on the line. They'll look for every advantage they can find.
What I'm trying to say is that if you automatically get cool special abilities as you level, you won't need to hand out magic items to make players happy. They'll still get cool powers, only now they're non-transferable.
Want to know one of the stupidest things about 3rd edition? Rings of protection +1. I'm playing in a Red Hand of Doom campaign, and we've so far lost about 7 PCs (three players never lost their characters, three players have lost a few). We now have a lot of spare rings of protection +1. Whenever a new PC comes in, he has his own gear, but he also gets to take the last guy's ring of protection. Then he cherry-picks the other loot: stat-boosting items, tons of wands and potions, and embarrassment of useless +1 weapons. My current character has a +1 returning harpoon. Why? Just because.
You suggested severely limiting the options for increasing power. That's what I want. Just make magic items a limited resource, so that very few enemies have them, and a hero can only have one or two.
I said before, I played in Conan, and I never thought, "Damn, I wish I had magic armor." Because in the character's mind, sure, there's some magic armor in the world, but it's owned by a powerful warlord. Getting that armor would be a quest in itself, and I'm busy trying to bring down a cult of scorpion-god-worshipers. I ain't got time for that.
If Conan doesn't need magic items, why does D&D?