Lawful means following orders, having a set of rules, respecting a hierarchy, giving respect to certain individuals because of their title and status. Chaotic means basing decisions on what you think best serves your goals, respecting (or fearing) individuals because of the power that they wield and not being beholden to external rules (although obviously you are aware that actions may have consequences).
I don't care what Gygax said 50 years ago, he had some strange ideas. But again ... I find alignment as useful or more useful than TIBF. Most people I've discussed this with in person either find it useful or don't care because everyone knows the difference between the standard depictions of Superman and The Joker.
If you don't find alignment useful, ignore it.
I do ignore alignment.
The problem that I see is that, each individual player or table may find alignment very useful, but it's so depending on that individual's or table's belief that it's
very hard for it to be consistent across the board. Like, would a Lawful person respect a high-ranking individual who is incompetent? (Or who isn't evil, good, or neutral enough.) Wanting to remove that individual from power and put a better-suited person in their place is at least a
bit chaotic, especially if there aren't any hard and fast laws for expelling someone from office. And a Chaotic person can have great respect for someone just because of their title and status, even if there's no actual power in that title. They just might decide that the highest-ranked member of the Pastry Chef Guild is more worthy of respect than the Queen, because the Master Pastry Chef is
really, really good at their job and clearly earned that title through hard work, while the Queen just had to be born to the right family.
And that doesn't even take into consideration people who play Lawful Awful or Chaotic Stupid or Neutral Boring.
Basically, while yes, I'm sure that you find alignment useful, I just don't think it's as useful as people think it is. I think people come in with a lot of their own decisions as to how individuals or societies work and only afterwards take alignment into consideration. (Seriously, how many people really play elven societies as Chaotic Good?)