In the beginning, there was one hero. At the same time, in another universe, there were four. Since then, the number has bounced around a bit, but three or four seems to be the accepted industry standard for party size. And why not? Those are good numbers. One fighter, one healer, and one or two other people who want to work hard for the money, so hard for the money. They're good for the battle, and they're good for the story.
Yet, somewhere along the way - maybe it was Final Fantasy 6, maybe it was a lot earlier, I don't know - other people started signing on. The party size didn't grow a whole lot, but that recruitment pool sure did. With that came a bit of a snag: what, oh what, do we do with so many people? How do we tie 8, 9, 14, 50 or 108 people into the plot when they're not all going to be there every step of the way?
This, of course, is not to discuss the logical inconsistencies of large numbers of playable characters - one of the most popular being "why doesn't the rest of my posse help in battle" or "why is the antisocial ninja or the womanizing drifter content to just hang out until we call him". This is merely to lay down something that deserves a little pointing-out.
Simply put, the larger the number, the less important the characters become.
By way of example: say what you will about Final Fantasy 4, but at any given moment everybody in your party is there for a reason. Though there is a sizable cast whom you control over time, and the merits of those characters are certainly debatable, you are still limited to whoever the plot deigns to grant you. For better or worse, they are not irrelevant. Even spoony ol' Edward, who (in a just and awesome world) would have been strangled by the Hitman while hiding off screen, had his reasons for being there. Contrast this with later installments (specifically 6), where the player has a significant amount of control over who goes where, talks to who and fights what. The trade-off for this flexibility is that the importance of any one individual towards the story is decreased, which can deprive the game of a strong central character (or core set of characters).
Preference for one over the other is not inherently wrong; like many things, it depends on the execution. Furthermore, there are indeed instances where party selection can be done without compromising a character's importance to the story. The Breath of Fire series is fairly strong in this aspect, as even when party members can be easily swapped, the small size of the total party works to keep them all reasonably relevant. There are exceptions, even within that same series (Dragon Quarter doesn't count as it's some kind of mutant spin-off that scientists are still studying while living the good life on the off-world colonies) but by and large smaller character pool sizes work in favor of developing each character.
Some, of course, prove this by going to ridiculous extremes, with mixed results. Few would argue that all of Chrono Cross's characters were truly necessary, important, or even interesting, and I suspect not many more would argue this for even half of them. Suikoden is another obvious target, and despite personal affection for the series (and that there's a reason for the high number of characters), I wouldn't dare to suggest that most of the playable characters (and most of the non-playable characters) were all that necessary to the plot. Maybe some army, somewhere in time was hurting for a bathhouse guy or a creepy winged guy, but I just wasn't seeing it.
It's not unlike a mathematical formula. The more characters there are, the less screen time there is go around, and the less any one character is needed to keep the ball rolling. Story, or versatility. There's room in the genre for both, but as we've come to understand them, role-playing games tend to need one more than the other.