In the final battle between Smith and Neo, we can see almost all Smith clones just watching the fight. Why didn't the rest of them join, wouldn't that make them stronger? Also, could it matter which copy of Agent Smith actually took part in this fight?
Smith is overconfident. In particular, the Smith that fights Neo is the Smith that was created by assimilating the Oracle, and the Smith/Oracle hybrid has foreseen that it only takes him alone to beat Neo.
Smith/Oracle: Mr. Anderson, welcome back. We missed you. You like what I’ve done with the place?
Neo: It ends tonight.
Smith/Oracle: I know it does – I’ve seen it. That’s why the rest of me is just going to enjoy the show – we already know that I’m the one that beats you.
Unfortunately for Smith, he doesn't understand Neo's choice of self-sacrifice at the end, and, I'd argue, he doesn't really understand his own choices. As the Oracle said, no one can see past choices they don't understand, so Smith didn't understand the consequences of his and Neo's actions.
Deus Ex Machina (the baby-faced computer that Neo spoke to) can take out all the Smiths based on Neo being assimilated by one of them, so I doubt whether it would matter which Smith took part in the fight from that perspective. From a story aspect, the Smith/Oracle hybrid is the one with the power of foresight. That, combined with what looks like the Oracle's subconscious influence on Smith before and after the fight, makes him the perfect one to decide to fight Neo.