It isn’t, generally, until the first primary is over that the nation wakes up and realizes that the presidential race has started. Having a series of primaries is therefore helpful, because it prevents the few most politically active from picking the nominee. There are other benefits as well.
The primary system, being spaced out as it is, lets less well-funded or known candidates to get to present themselves to the voters. In a national primary, the candidate who happens to have the best name recognition at the time of the vote (Howard Dean in early January, most likely) or who is leading in the stupid horserace polls that dominate so-called “television journalism,” would win.
Putting the first primaries in small states puts a unique pressure on the candidates to actually present themselves and interact with the voters in a very real way. The voters in Iowa and New Hampshire are wonderfully cynical about polls and candidates, and do a good job of vetting these people. Even if they don’t always pick the eventual winner, they do a good job of knocking the front runner off base a bit, preventing an out and out coronation, which is what a national primary would be.
Spacing out the primaries also allows one of the candidates to build momentum, and eventually win a majority of the delegates. In a national, six-way primary with more than one or two reasonable candidates, you could easily end up with no delegate majority for anyone, and thus a brokered convention.
Which is not to imply that the current situation is a panacea. I would prefer to see it more organized, and for it to go on longer.
I would, as others have suggested, break the primary into ten elections, with five states (and various territories, DC, etc) in each. The primaries would be organized based on the population of the states in question. The five smallest states would vote first, then the next five smallest, etc. This would spread out the season, keep the early contests in the states where there’s a chance for less-well-funded candidates to emerge, and where the voters can inspect candidates in person. It would also keep the contest going for a long while, and give most states a chance to have their say, since it would be impossible for a candidate to accrue a majority of delegates until very late in the game, possibly the last round in a contested match up.