I don't understand this. I'm good enough to win fights with or without items. It's that simple. In what I've seen, whether items are on or off has no bearing on a player's skill; the same people who win do well. The people who do badly do badly. It's not like I'll win five fights in a row and then as soon as items are turned on my opponent starts winning.
So what if they appear randomly? Oh, look, a crate spawned above me. I'd better dodge to get out of the way. Action/reaction. Simple as that.
You say that items throw off the balance of the game badly. Personally, I never see this happen, because all of the items themselves are balanced. The home run bat does ludicrous damage, but it's slow as all hell. A good player can avoid that. The fan is quick, but does low damage and has low stopping power. But it can break shields. The star rod has projectiles and bludgeoning capability, but its projectiles are slow-moving and have a large charge time. THERE IS A COUNTER TO EVERY ITEM. USE IT.
We're not talking about instant-kill rocket launchers here, folks. These items fit within the game because they themselves are balanced. It doesn't matter if they appear randomly.
Chess is completely, 100% based on strategy. Putting items and stuff into it would be completely ridiculous. But this is Super Smash Bros. we're talking about here. It's not like the items make no sense within the game's context.
What you're saying is that items give characters abilities they shouldn't have had earlier. But EVERY ITEM HAS A WEAKNESS. Look, Marth is a close-range character. Now he has a ray gun. So, yes, he has a capability he didn't have before. But, the ray gun has the same effect as with any other character. Other players can defend against the projectiles. It's not like Marth gets a super-power ability with the ray gun that no other character has. It's the same damn ray gun. Counter it.
And by the very nature of random items, it ensures fairness. Do you think it's possible that one player will get every single item every match? No. Also, battles over coveted items also provide a bit of strategy. Do I make a run for the beam sword, or take a defensive stance? It adds mind games.
The chess analogy doesn't work simply because chess is designed to be a completely strategic experience. Items fit within Smash Bros.' context. Every one has a strength and a weakness. Use them to your advantage.