Wow,a great question about an iconic record.
This is an interesting read - https://www.loudersound.com/features/king-crimson-how-we-made-in-the-court-of-the-crimson-king
But, it doesn't answer your question. It does help to know they were self-produced in an established British studio. The Beatles success would have broken the traditional mold for popular music by then so it was possible to break rules in hopes of success. Apparently they got a flexible and creative engineer, although I doubt the engineer really knew exactly what he was listening to, it was unprecedented and still boggles.
I put my headphones on and gave a close listen on YouTube. To truly know it you'd need a high quality vintage tube stereo system (dammit, I miss my old British made Wharfdales!!!!).
First, it sounds to me like Greg Lake is too close to an excellent microphone, there is quite a bit of sibilance but the lyrics are still clear. The consistent volume indicates a limiter clamping down and an overdriven tape recorder. I used to hurt much less expensive ones and they had that fizzy but define tone when pushed.
I vote for intentionally "bad" technique for the sake of creating an effect. They didn't have all the fun stuff we have now, you had to hurt things to make them howl and scream.
And now, a memory. I was 15 and in a band. The lead guitarist was also a good keyboard player. He'd had lessons and did his homework. My Mom got us booked for a proposed "Rock Mass" at the Catholic church that was across the field from the family home, a 200 yard walk at most.
I remember we played Crossroads and a Jethro Tull song. I was on bass, had a tiny idea what I was doing. We got permission to use the church's pipe organ, which was a grand thing indeed. So, I was the second best guitarist and switched to guitar. The vocalist switched from strummer to bassist and the lead guitarist became the organist and played the solo on The Court of The Crimson King.
That might have been my greatest moment as a musician, with thousands of gigs behind me - just holding a Gibson SG and listening to that pipe organ.
Let's see who else chimes in and what they say!!!! Cheers, Kuru