So I operate more in line with how you do, but having tried some organizational systems I think I understand the "second brain" people.
One, it forces you to do a crude approximation of critical thinking. It allows you to examine and organize your thoughts, either physically or digitally. It isn't the same as being able to sit and break something down in your mind, but for those who struggle with that, a "second brain" allows them to reap some of those benefits.
Two, it allows you to turnover things quickly in your head. By training yourself to immediately dump out an idea into an organizational system, you don't have to hold so many things in your head. Furthermore, words are immutable and the thoughts in your head aren't.
But for me, the good thoughts usually rise to the top. And there are a lot of things I'm thinking about that are so vague, it's just a feeling. And trying to write those down robs those thoughts of the long term, "on the backburner" mental processing they need to become actual ideas. They're thoughts that are still in the embryonic phase. I can't write down the qualia of them, and when I try to I move them into a "second brain" I lose it.
I think organizational systems are work dependent. Running a business lends itself well to an organizational system. Where it's good to try a lot of shallow things. But something like physics, for example, requires playing with ideas in your mind over a long period of time until they become solid enough to chase more seriously.
I think programming probably straddles that line and it depends on what you're doing at any given time.