I'm seeing a lot of arguments in this thread coming from people who base their arguments on experience from other metagames. The biggest example of this that I've noticed is from VGC players, so while I love VGCs and respect that metagame, I'd just like to explain why experiences from the VGC metagame aren't great justifications for a change like this.
First, VGC teams are smaller than Smogon singles teams. When you're only using 4 Pokemon per battle, it's going to be a lot easier to maintain diversity in your choices. Smogon singles have 50% more members per team, and so there's a 50% greater chance that you'll have to adjust a set because of duplicate items.
Second, VGCs are based on doubles instead of singles. There are many items that work much better in doubles than singles and vice versa. Take, for example, Leftovers. Most of the time, defensive Pokemon in Smogon singles are going to be staying in for well over 4 turns. This makes Leftovers far more efficient in the long run than something like the Sitrus Berry. This passive recovery is extremely important for not only healing damage from attacks, but also for mitigating passive damage from entry hazards, status, weather damage, etc. In Doubles, however, many Pokemon aren't going to live more than a couple of turns. This makes the Sitrus Berry much more efficient on bulky Pokemon for surviving that second attack. Another example is the use of Gems. In singles, Gems occasionally have a use on sets trying to nail a certain KO (SubSD Rock Gem Terrakion) or trying to abuse Flying Gem Acrobatics. However, it's usually better in the long run to use a Life Orb or Choice item for the extra damage over time. In Doubles, the fact that many Pokemon don't survive for very long makes that one-time 1.5 boost a lot more efficient.
Third, VGCs are much more offensive on average. It's really hard to wall your opponent when you're facing down two Pokemon at the same time. VGCs are far more offensive, but as has been said before, offensive teams don't suffer that much from an item clause because of the raw number of items they can abuse effectively. For example, I can build an offensive team with Pokemon like Scarf Genesect, SubSD Rock Gem Terrakion, Life Orb Landorus-I, Choice Band Dragonite, Choice Specs Latios, Double Dance Landorus-T with Leftovers, Focus Sash Alakazam, Expert Belt Keldeo, Fighting Gem Breloom, Custap Berry Skarmory, etc. and not repeat a single item. On the other hand, defensive teams really need Leftovers. The passive recovery is essential for constantly dealing with attacks and passive damage. You can use Black Sludge as a replacement for some Pokemon (although that would force you to run a Poison-type, a thorn in the side of the "promoting diversity" argument), and some modern stall teams run a single Scarf user, but that still leaves you with 3 other slots for Pokemon that would really want those Leftovers. Sure, some of them can make do with some other items, but there's a reason defensive Pokemon usually run Leftovers: it's simply the best item available for them. By forcing these teams to use other items, you're forcing them to run sets that are worse off than they would be with Leftovers.
This point about defensive teams brings up another big issue about improving diversity. First of all, you may think that making people run different items will make the metagame more diverse, but it really won't. Most of the sets will still be the same, just with less than ideal items. As I explained before, an Item Clause will also put a lot more pressure on defensive teams than offensive ones, even as defensive teams are already suffering more with each subsequent generation. This will cause offensive teams to continue to dominate to an even greater extent, and as defensive teams get less popular while offensive teams get more popular, the diversity of the metagame will decline. This whole "promoting diversity" argument just doesn't hold water.
Can't we just compare and contrast the Smogon-meta to the Nintendo-meta and see which one is better?
Realistically, since they both already exist, can't people who prefer item clause just play Nintendo meta?
There's a lot of wisdom in this statement. Smogon and Nintendo are two very different entities with different purposes. One of the great things about these differences is that they give you distinguishable choices. If you prefer options like 3v3, Item Clause, no Evasion/Sleep Clause, and level 50 battles, you can enjoy Nintendo's Wi-Fi metagames. If you prefer 6v6, no Item Clause, Evasion/Sleep Clause, and level 100 battles, you can play on Smogon's simulators and have fun there. Changing rules we use here for the purpose of conforming to Nintendo is pointless because there's already a medium in which you can enjoy those rulesets, so there's no need for us to provide one. When we make changes, we should do so because they are in the best interest of the metagames designed and maintained here. Now, if there suddenly becomes a surge of broken strategies involving multiple copies of certain items that could be fixed by implementing an Item Clause, I say go for it. Otherwise, I'd rather give players the freedom to run whatever items they wish.