You can start by trying to live in reality rather than adhering to this cult of Gygax?
Well, ok, first you need to understand that the game isn't happening in reality. In reality, you can't take a tiny ball of bat guano and sulphur, chant the right magic words, and conjure 40' balls of flame. In reality, there aren't four elements that everything is made of. There are lots of things about the game that are different than in reality.
The fact that you would describe people as not adhering to these 9 artificial boxes as being a failure of their Wisdom or Intelligence demonstrates a real failure to understand how humans work.
Once again, we aren't talking about reality. We are talking about a fantasy universe. But what I describe regarding Wisdom and Intelligence informing how people relate to the their most fundamental beliefs regarding ethical and moral behavior has parallels in the real world. For example in the real world, a person might be a Sikh, or a Jain, or a Hindu, or a Budhist, or Sufi, or Christian, or a Logical Positivist. The more intelligent that person is, the more we would expect the person to have worked out a coherent, all encompassing philosophy of life, based around what they believe. If they are a theist of some sort, we'd expect that person to have a adopted a very complicated and nuanced theology explaining to them every aspect of life based on their fundamental beliefs. They will have questioned and devised answers and have sophisticated responses to practically any question regarding how one ought to behave given what they hold to be true. The same thing applies to our fictional fantasy characters. The more intelligent they are, the more complicated and extensive will be their understanding of how a moral principal like Lawful Good or Chaotic Evil is. A less intelligent Chaotic Evil person probably isn't capable of elucidating what they believe. They just act on impulse and only give the most simple explanations for their behavior. But intelligent CE person could give complex rationales for their behavior, so that their own behavior seemed right in their own eyes and was consistent with the way they believed the world was or should be.
In the same manner, not everyone in the real world - even if they understand what their beliefs demand of them - is consistent in applying that understanding. There are always areas of their life that appear to a greater or lesser degree to be in conflict with what they say that they believe. The less a person's life seems to be in conflict with what they believe, and the more discernment that they show, the more self-control that they have, the more consistent that they are in their behavior, the more we say that person shows Wisdom (particularly if their beliefs are somewhat congruent with our own beliefs). In a religious context this is often called piety. In the same manner, we'd expect that the wiser a D&D character is, the more their actions would take into account what they actually believe and be consistent with it. We'd expect them to more often intuitively understand how they ought to behave according to what they believe in even difficult situations.
Following this yet?
"Lawful Evil" is not someone that someone sets out to intentionally be.
Well not in this universe.
Their beliefs are never going to be perfectly "lawful evil" Not in reality or anything written remotely close to it.
Well, this isn't reality we are talking about though, right? It has elves, dragons, magic, dwarves, and fairies. It's not reality.
Maybe that is the way you live as you have been inducted into your little Gygaxian cult, but it is not something people are going to adhere to if they are created and act independently of any awareness of Gygax's little boxes.
Again, I am not a member of anything like a 'Gygaxian Cult'. I'm just describing a game and how you play that game. In reality, I have a very different set of beliefs about how the world works, that don't rely on game concepts. Now, I enjoy playing "What if?" games with these game concepts, because they can lead to interesting discussions and interesting ways of looking at characterization and mythic archetypes and literary techniques and philosophical conflict, but I don't actually believe that these are real, because I understand that we are just talking about a game. Indeed, one of the things that I like about the whole alignment system is despite some correspondence to real world beliefs, we aren't literally talking about anything real people believe in, so we can neatly avoid talking about things in real world terms and the all the problems that come with talking about real world religion, politics, custom and so forth.
One is classified as Lawful Evil because though they believe in following the following authority or the general guidelines the collective has agreed upon strictly, within that framework they choose to do a good deal more selfish things than altruistic things. They are willing to enact suffering within the world in the name of adherence to the overall order of society or so long as it benefits them... to a point.
That's like mostly right but not perfectly right. It's the sort of construction I'd expect you to have from reading 3e material on alignment. In particular, it avoids problems like how we classify Kamikazi pilots or suicide bombers or Nathan Bedford Forest or really anyone who is loyal to a code or idea that we'd want to classify as evil, but who has self-sacrificial evil and who actually holds the society, group, or ideal as more important than themselves. But, that's a minor point, and again, I don't want to discuss it in real world terms because that will quickly lead to passionate arguments about what the real world is actually like, rather than merely what this fantasy world is actually like.
But there is going to be a point. A point where the amount of suffering they are causing is greater enough than the benefit they gain from it or continued support of the order and one's personal benefit come enough into conflict that one ultimately has to prioritize one over the other. This is not a failure of "intelligence" or "wisdom" because never from the start were their ethical code defined by "Lawful Evil" as they are not adherents to the "one true Gygaxian faith" like yourself. They were simply labeled "lawful evil" because that was the one of the 9 boxes that seemed to best contain their morality.
It's really hard to reply to any of this because your starting from such an erroneous place, and making this personal. Again, just because I can talk at length about the nature of a fantasy universe, doesn't in the slightest that I believe in elves, dragons, magic, or Lawful Evil. Gygax is a game designer who I have a lot of respect for, but my actual real world beliefs are much more like Gygax's actual real world beliefs - because he didn't actually believe in elves, dragons, magic, or Lawful Evil either. To him it was just a game. In any event, the particular confusion you are having in this section - beyond thinking that I actually believe fantasy is real - is that your definition of Lawful Evil had a flaw in it.
I'm going to stop here rather than turning this into a Fisking session, because most of the rest of your complaints again have to do with poor understanding of the system, and only when we fix your basic understanding of the alignment system can I meaningfully talk about the points you raise.
Those boxes were just weak sauce attempts to define people's morality and only work in cases where you have presupposed those boxes exist and have them act according to one. With any other fictional character, you go through a gamut of stories and there will be no universal consensus as to which box they fit into.
I don't know how weak sauce they are. I know no other games attempt to classify and gamefy morality and ethics that has generated anywhere near as much discussion. And of course, yes, the system only works where you first assume that the system exists as a set of moral absolutes within the game universe. It doesn't however in anyway require that you believe that the system exists in the real world or even that moral absolutes exist within the real world. However, there are typically strong consensuses that are built around classifying fictional characters. It is usually not perfect consensus, but usually strong consensus is built in community regarding the alignment of any fictional character. Almost everyone agrees that Superman and Captain America are consistently portrayed as Lawful Good, for example. Even in the case of a character like Batman, where famously you can show the whole alignment wheel and put Batman in every box on it, there is still strong consensus that the particular Batman in the box belongs in the box and fits in the box, or that demonstration wouldn't make much sense. In fact, what's going on in the case of a character like the Batman is a couple of complicated biases are interacting, the most important of which is the bias of the author regarding what motivations and behavior would be most interesting for the Batman character. So you see the Batman portrayed very different by different authors over the course of the last nearly 80 years we've been writing stories about the Batman, and those different portrayals make for different characters with different beliefs. The other complication here is the bias of the reader, which will tend to want to interpret a character - particular a character that they like or find interesting - according to their own biases. That can either happen because have really flawed understanding of the alignments like "works outside the law, so must be chaotic", or it can happen because in some fashion their own real world beliefs overlap areas of the fantasy beliefs causing them want to assert their real beliefs as 'right' and 'truth' within the fantasy system. That's what I call 'spinning the alignment wheel until your beliefs are at the top'. So for example, real world Objectivists have beliefs that in some ways overlap the fantasy alignment Chaotic Neutral, and when you pose Chaotic Neutral in terms that are recognizable to Objectivists as being somewhat congruent to their beliefs, they tend to want to spin the wheel and say, "No, those beliefs are Neutral Good, because that is the right and proper way to view the world." So to some extent you need to be able to back out of this toy morality we are looking at and view it objectively as a toy that exists for the purpose of the game, before you can talk about it meaningfully.