Well I don't think the music theory people actually think Johnny Rotten was sitting around thinking, "you know what mate, this bleedin song needs an augmented triad!" they're just trying to fit actual music to music theory, which is complex (and interesting).
That said, there’s some legend and a Guitar World interview about how Clif was the theory guy in Metallica: https://www.rocknrollinsight.com/2017/03/cliff-burtons-influ...
This discusses some timing anomalies in some Metallica music and also seemingly refutes the point that Clif was the Master of their Puppets https://metalintheory.com/metallica-and-the-case-of-the-miss...
Overall, I used to like Metallica as a kid but I hated what they did with the whole Napster thing enough that it inspired many years of amazing torrent community interaction that has brought me so much musical joy and good times. I also despise some of their decisions around mixing / overall sound of albums like Death Magnetic given that their own personal amazing rehearsal spaces are fully kitted out with Meyer Sound systems, which are fantastic and arguably the best in the world, yet their music sounds like that. Perhaps all those years playing have wrecked their ability to hear anything over 6khz.
The punk guys couldn't care less about music theory or whatever, they cared about having fun with the music and playing skills were almost irrelevant, almost frowned upon (you don't hear a lot of guitar solos in punk - it's mostly 3-note, fast paced music with rebelious lyrics... I feel so old describing it like that :D ). For a time, "broken" timing was in vogue, both in some punk bands and in a lot in metal (not sure if Metallica was a pioneer with that? I am too "young" to remember).
The metal guys were not completely different, to be honest, except for playing skills being much more important, as it's integral part of the music to have endless solos and complex riffs... but at least in my circles it was more about raw skills (how fast you could play more than, say, how much "feeling", though that was important too) than theoretical knowledge.
I have never been much of a fan of punk music but I love the punk aesthetic. That mindset really extends to so many things.