How the hell do items make a game more balanced? They are RANDOM. You have no idea what you're talking about.
It's becuase how Smash Bros is balanced.
The truth is the game is balanced. But not for 1v1 gameplay. The game is designed as a 4 player fighting game, so naturally this is how the game is balanced. Link is the best example. He was low in 64, and a mid/low in Melee, so why did they make him worse? The reason was he was actually over powered in Melee. Shocking, I know. In the 1v1 field, we was meh at best, but in 4vs he did amazingly well. He had projectiles for camping, and some really mean attacks, the spin attack especially. So come Brawl they make his recovery weak, lower his air speed and gimp the spin attack. Now, in a 4vs environment, he is balanced. His weak recovery offsets his power and attack speed. If the game was balanced with 1v1 in mind, they would have done more to make him stronger.
If you play in a 4vs environment, you'll see everything come together and the game be a lot more playable. But why is it that the game isn't perfect, and every character on an even playing field. Because they didn't balance it like they. What they did is basically make every character have enough pros to have them be usable, and in capable hands, the character can win. This is why items help balance. Because it gives every character an opportunity to win. Instead making it a combination of random luck and skill with the item.
Now, what happens when you try to make the game tournament ready, the balance breaks. No longer is it about all the characters being usable, but the characters needing to be on a flat and even (read:balance) plain. This wasn't the intent of the developers and, as such, all falls apart. Another big part is that some characters are naturally better at 1v1 battles. In Melee, Fox's trophy says that he is better in 1v1 battles. It comes as no surprise why he was top in Melee. His trophy even said so.
The big problem with competative smash is the game was not designed for it. In numerous other fighting games, they can reach a balance. Since the games are a lot more tame, they can focus on traditional balance, and also please everyone, having the game be easy to play but hard to master. In Smash, they have to make it balanced for 4vs; doing it any other way would make 4vs imbalanced and, consequently, isolate the majority of fans.
Of course, even if Smash could be balanced with tournament play in mind, there would still be tier, and becuase how the fan base acts, one character is going to be "overpowered".