Alignment['s] purpose [is] to segregate player characters into factions or teams which might then complete for treasures and territories within the campaign milieu […] alignments are factions, and not just ephemeral, distant, cosmic factions meant for celestials and deities and eldritch things beyond the ken of mortals. Alignments are factions that player characters belong to, and which form around player character parties that exist in competition with one another within the same campaign milieu—more analogous to sports teams than to moral philosophies or religions.
An example of the proper use of alignment would be a campaign that has two separate groups that meet on different game-nights. One party is Law; the other is Chaos. (Any characters whose players show up inconsistently and might join either party on an adventure are Neutral.) Perhaps from the perspective of the first party, they champion Order and come from a well-organized empire that views barbarians from beyond their borders as agents of Anarchy; while the second party represents those very barbarian tribes, valuing Freedom and seeing the empire as Tyranny. As each party delves their way into a dungeon that exists in the mountain range separating the empire from barbarian lands, many weeks or even months of play may go by before the two teams even become aware of each other; but conflict will inevitably arise, especially once high-level player characters emerge—Lawful lords, patriarchs, and wizards who see the barbarian lands beyond the border as wilderness ripe for settling and colonization, and Chaotic versions of the same who desire to invade the empire in the name of “liberation” (and plunder).
Ultimately, alignments should be worked into the foundation of the milieu, but they should also be allowed to arise naturally through play. If a campaign only ever has one consistent adventuring party, there is no need for alignment—because the only meaningful player character faction is “the party” (as opposed to the DM); most characters (with the exception of priests and knights) can safely remain unaligned. Conversely, in a very popular and long-running campaign with many different adventuring parties, it may become necessary to divide existing alignments even further. Law and Chaos may become riven with internal strife, and parties may over time divide themselves into Lawful Good, Lawful Evil, Chaotic Good, and Chaotic Evil (or some other suitable division).
In general, most 1st level characters should begin the game unaligned, only declaring themselves for an alignment as it becomes relevant to gameplay. Priests and knights are an exception: a priest must declare for an alignment in order to surpass the 5th experience level, and a fighter must likewise be aligned in order to become a knight. Ultimately, however, it must fall to the player to decide when or whether their PC is to align with Law, Chaos, or Neutrality.
Alignment and Multiple Characters: The harsh penalties inflicted on a character for changing alignment [q.v. the DMG 1e] exist for much the same reason that multiple characters belonging to a single player are always absolutely forbidden from sharing treasure, magical items, spells, etc. with each other. It helps to enforce a strict separation between player and character that prevents a player from accruing undue advantages purely because of their controlling multiple characters. If, for example, one has a player who enjoys playing Chaotic PCs and is solidly on “team Chaos” in the campaign, it would not do for this player to create ostensibly Neutral or Lawful PCs who could join “team Law” but then work to subvert the Lawful party as a “mole” or “plant.” Such a character would have to be Chaotic from the start (and therefore at risk of alignment detection in-game). For the character’s in-game alignment to be Law or Neutrality, only to have them “defect” to Chaos at a later date (when this was in fact the player’s true intention all along), must be discouraged by solidly defined mechanical penalties, purely in the interest of fair play.