As mentioned before, I don't see how we cannot do exactly the same analysis on your own proposed metric.
There is only one metric: group versus individual. Thats it. Not nine metrics unhelpfully confused under one label. When the metric gets used, it means something.
A Lawful person can be solitary. Holding true to the spirit of the rules when everyone else is cheating is almost definitionally lawful, despite being both a common trope and, sadly, actually a real life event in many cases.
There is such a thing as "the last of ones kind", but it is unsustainable. By definition, the group ends with that individual.
If there is a solitary individual with the Lawful alignment, that alignment is meaningful and conveys information. That person is a group. Perhaps one day that one does run into someone else who is also a member of that group.
A Chaotic person, as you yourself note, can form a group and seek solidarity. They just do so as a free association; in the ideal Chaotic group, no one is "bound" to stay, but each stays because they wish to, with no coercion felt or implied. (Also, I find it very humorous that you consider opportunities a group thing when...well, opportunity seems definitionally personal to me.)
Chaotic people want to be oneself. They want other people to be their selves. They seek companionship, but not conformity.
The only difference is between adherence to consistent and predefined rules (you can't "play by the rules" if there are no rules to play by) vs evaluating each choice as it comes (freedom from coercion means...pretty much exactly that.)
No, thats not it. It isnt about coercion versus noncoercion. It is about group versus individual.
Lawful is about identifying oneself as a group. If group succeeds, the member feels the success, and if the group suffers scandal the member can feel extreme pain. The sense of self - who one is - is wider. As long as the group survives, the member is in some sense alive. The group can be a family, clan or tribe, a place or nation, the community of a sacred tradition, a gender. Any group that deeply defines ones identity.
But both identities can be internal or external ("the law of the land" vs "truth is not decided by popular vote,"
Yes. A Lawful person can happen to be away from the group that defines that person, but the person feels the loss, like they left their arm or leg back there.
The Chaotic person can be social and cooperate, as long as it is on that persons terms, and that person has enough space to be oneself. The Chaotic person cares about other people, but not about being other people. The Chaotic is person is a nonconformist. It is statistically less likely that the Chaotic will happen to want to do something that an entire group is pressuring, obligating, and coercing to do. Indeed, that kind of pressure is often off putting, even if the Chaotic did want to do it.
When dealing with a Chaotic, one must respect the agency of that person. When dealing with a Lawful, one must respect the group of that person.
Of course, most humans are mix of group identity and individual identity. Hence D&D humans tend to be Neutral. But there are groups and individuals who lean toward one of the extremes.
Not sure if the following is accurate animal science but: dogs feel Lawful, as each one is ones pack, and cats feel Chaotic, as each one does ones own thing together.
I do what I need to do, can be why Lawful person conforms and why a Chaotic person nonconforms. The self-identity is a need.
vs "you'd do the same for me") and both can operate as individuals or as groups.
Yeah, "Youd do the same for me", can be two Chaotics supporting each others differences, or two Lawfuls sharing each others same identity.
A further benefit: these conceptions ("Lawful" as "adherence to consistent and predefined rules,"
The rules themselves can be Chaotic, like Freedom of Speech. Each individual has a right to spesk ones own mind.
"Chaotic" as "evaluating each choice as it comes") are actually consistent with the descriptions you referred to as "unhelpful," meaning we don't have to completely discard the descriptions and advice given by the books.
A Chaotic individual can be - and often is - consistent. But is nonconformist.