Actually, I totally agree with this, but that doesn't change the fact that the game is saturated with items that just aren't very good. You have to give me story reasons to want them, because the mechanical reasons (outside the basic +) are underwhelming.
And while your suggestions of adding story and lore to items are good, they don't address the fundamental problem. Let's say I have a Tiefling fighter built with feats designed to compliment my attacks with a +2 Flaming longsword. You, my DM, design an amazing series of quests that culminates in me defeating a bad guy and winning a +4 Frost longsword named Blueballs (which would appeal to me greatly). Still, I find myself looking at the feats I've taken that enhance fire accuracy and damage, looking at the amazing Blueballs, and saying, "Thanks, but..."
I realize it looks like I'm talking out of both sides of my mouth here, but the issue is that if I build my character around a particular item, it's so good that I'll never want anything else; if I don't, very few things are good enough to make me care about them at all.
I don't dispute that there are ways for a DM to combat the problems, but it shouldn't be required. I do think the rarity system is a step in the right direction, but it also highlights how "meh" a lot of the uncommon items are.