Why should I keep one of every item?

There are a few reasons to keep items in your inventory, but there's no hidden mechanic or reason to keep items that you are truly done with. Reasons to keep items are:

1. Achievements There are achievements for having N items in your inventory and for mastering items.
2. To master them and gain XP. Mastered items grant bonuses upon their first mastery and sell for double the value of the unmastered item.
3. The Infinity Blade is the key to some extra bosses and stuff.
4. Variety. It's a weak reason, but having equipment with a variety of special features, elements, etc. might be useful if you need to farm certain things or need certain abilities for certain fights.

So if you are collecting achievements, keep as many as you can and then feel free to sell away. To max your character and maximize the value at sale, keep items until mastered and then you can sell them. Do not sell the Infinity Blade even once mastered.