Why not 4d6-drop-lowest or some other method of generating superior scores? Because you scrunch the range of likely scores toward the top of the curve, which naturally produces a less diverse spectrum of abilities.
Why in order? Because when players can arrange scores to taste or even swap one pair, it tends to make characters of the same class look very much alike. Suppose a player rolls scores as follows:
She wants to play a fighter. If she can swap two scores, you know with almost absolute certainty that the 16 is going in Strength and the 11 to Wisdom, because that's what a fighter is "supposed" to look like. If she has free rein to arrange the scores any way she likes, the 8 probably won't stay in Dexterity; it will likely end up in Charisma; the 13 will probably be assigned to Dexterity or Constitution. The odds are that any fighter character created with these options is going to have its highest score in Strength, and any other higher-than-average scores will probably wind up in the other physical abilities. Fighters will start to look very much alike in their stats, and it may even create a perception that any fighter that doesn't conform to the pattern is inadequate or inferior.
If the scores must be played in the order in which they were rolled, our hypothetical player is faced with a healthy dilemma. Does she play a wise but physically average fighter, or opt for a cleric? There's no reason she couldn't choose to play a magic-user, thief, elf, or dwarf either.
This is especially true if we can somehow dispel the attachment to the concept of Prime Requisites for character classes. Sure, Strength is of benefit to fighters, but it benefits anyone who engages in melee combat, and a fighter can benefit from other abilities. In truth, every ability score can be of use to every class if a player plays the character in ways that capitalize on its strengths, whatever they may be. A character with a class-atypical distribution of ability scores can still be effective, just perhaps in a different fashion than the high-score-in-prime-requisite model. With the notable exception of the magic-user, who really needs at least to be able to read to study spells, there's really no compelling reason why any class needs to be so strongly associated with a single ability. (And even in the case of the magic-user, one might struggle along with a semi-literate 6-8 Intelligence. There's even literary precedent for dull-witted wizards - think Crabbe and Goyle in the Harry Potter novels.)
3d6 in order is a more organic way of growing, rather than building, a character. People are born with an array of strengths and weaknesses and choose their courses in life in light of their physical and mental makeup. Sometimes their passions and their talents don't align, and they must choose between following their hearts and pursuing their aptitudes. They don't get to maximize their builds; they must learn to work with what they have and make what they have work.
The choice facing our hypothetical player and her character already provides a huge opportunity to establish a personality. Does she follow her dream, determined to beat the odds and become a renowned swordswoman, or does she resign herself to the life of a priestess? If she does choose the path of the warrior, she's unlikely to be a statistical clone of any other fighter in the party.
Ability score bonuses can certainly be advantageous in play, but slavish adherence to a class/ability template is limiting. In truth, a bonus or penalty, even in a prime requisite ability, is rarely going to make the difference between a character that's fun to play and one that isn't, nor between success and failure in a chosen class.
The diversity that naturally results from 3d6 in order character creation, and the choices that in turn stem from it regarding class and characterization are, to me at least, far more interesting than cookie-cutter characters who are always exceptional in their field, to the point of making the exceptional tedious.