If there are only a dozen or so items, it becomes pointless to have then at all. If you only have a dozen items then you wouldn't have items like a buckler or the +6 damage claws. You'd have items like daedalus and heart of tarrasque. You wouldn't have 20 different options for attack damage. You'd have 1 or 2 options for each role. And at that point they aren't options they are mandatory. They don't become gameplay options they become hurdles. At that point just roll the items into the heroes themselves and be done with it.
I'm trying to articulate an answer that isn't "are you fucking stupid" but since I cannot seem to find one, I will instead make a list of a dozen or so items, then ask you if you would always take the same items out of this list with a given hero depending on the state of the game, the map and the enemy team composition, using dota items examples:
Rapier(pure damage item), BKB, Blink Dagger, Boots of Travel, Mekansm, Sheepstick, Blademail, Heart of Tarrasque(pure tank item), Satanic, Aegis, Dagon, Veil of Discord(or something similar, basically spell damage scaling).
You would ALWAYS pick the rapier and the heart on a carry, or the rapier and bkb? You would NEVER consider satanic, blink, sheepstick, dagon or aegis? Cause that sounds like fucking bullshit. That's a dozen of items, as in 12. You could add 3-5more without making it confusing with other effects, maybe variations like mjolnir as a DPS variation and AC as a tank variation, pipe, smoke, deso and any interesting item from other games too like an aoe movespeed item(similar to axe's ult movespeed proc when you kill something, short but high speed burst for the team).
But even with those 12 you have plenty of room to make different item builds even for the same role with the same hero depending on the team setup. While you would often take the rapier on a carry, you might have to take it as your second item instead of your first which already makes a variation, and in some cases you might be forced to not take it in favor of survivavibility and/or because your team doesn't need to be the super carry but instead to actually be able to not die instantly.
As pointed out later in the thread though talents seem to do some of the item stuff I'd want so it's probably not necessary as a system.