We already have the "mafioso" stereotype, so why do we need LE? Are all mafioso LE? Are there no NE or CE mafioso? Barghests, cranial rats, and displacer beasts, and hellwasps are LE- does that mean they all act like mafioso? Maybe nafioso is a better alignment than LE?
I don't need an alignment to tell me a CE monster might attack on sight, or might not; might be difficult to reason with, or might not. How is this helpful information?
Are all LE mafioso? Nope. But they share some of their "qualities"
LE is about yourself in a group. How can you make the group work for you and how you fit in the group. LE organisations and individuals are hard to infiltrate because they are coordinated. Cranial rats will have sentries and will work well within the group. Sometimes evil is only about how the creature will act toward other races. In the case of Cranium rats, they might care about each others but certainly not about other species. Their goal is to eat all. Even resorting to canibalism if needed because food is scarce. For Cranium Rats, I would refer to the novel RATS from James Herbert. An excellent novel that will show how LE critters might think.
LE humanoids might be organised (at la hobgoblins) with sentries, defined tactics and so on. But each and every hobgoblins strive to be one day the boss. They know their place but they will wait for a good opportunity to do it. They might respect the chain of command, but friendly fire happens sometimes. That is why most leaders of LE do lead from the rear.
Whereas the CE version would be easier to infiltrate. They rely on "I know who's with me" for security. They will have sentries, but these sentries might be a bit lax. Sleeping on duty, playing dice/bones, or doing all sorts of shenanigans but their duty. The CE will strike down the leader as soon as it feels it has a good chance, especially if the leader appears weak and the CE will do it, oblivious to the consequences. Where the LE might do it near victory to ensure that its side wins, the CE might do it as soon as the hated/feared leader is wounded. Both might cost the victory, but the nuance is clear enough.
And the NE? Anything between and at these two extremes will work. The NE do not follow a leader because of fear or admiration. It follows the leader because it suits its need. These needs might range from the chance to kill, get treasure, or souls. Who really cares. NE is in for itself but can show restrain if need. The CE will not.
And stats will influence the actions too. High wis or int will affect how a LE, CE and NE will present themselves. As a 20 intel CE foe, you might be likable (if of at least average cha) but it does not mean that all your underlings are. Demons would have won the Bloodwar by now. Their leaders are feared, intelligent and sometimes wise. But Demons are demons and following orders is not their nature.
And the beauty of this is: " I only extrapolate from two letters LE, NE and CE." Anyone playing with alignment will come up with these with more or less details and emphasis. But the basics are there.
@Oofta might play LE a little bit different, more honorable, less devious depending. But I am sure that I am relatively close to what he sees. Same for @Celibrim,
@Maxperson,
@Lanefan and many other posters.
Again, alignment is a basic system on how to play the basic tendencies of a character or NPC. It is not the only defining factor of personality and motivations. That is another part of the game entirely. I do not put motivations and full personality on shmooks my players will encounter. But I will for major foes, allies and recurring vilains. These two letters just help me play out NPCs with flavor in a pinch.