Well, let's go through the logic... timing makes the biggest difference at brown and black belt? Ok, so I'll move at exactly the right times doing techniques that aren't improving much from purple belt and they'll work really well against other people with presumably great timing and understanding of my purple belt level technical knowledge?

No, that's not it.

Timing of techniques Depends on knowing of the correct technique to achieve the desired goal. The perfect technique for the job presents itself Only by understanding the technical advantages of using it properly at a given time. When the timing becomes tighter, the technique must be crisper and more mechanically sound to be efficient at that increased speed and to be functional against someone of the same speed and timing level. But,... the answer is the same, timing depends on technical knowledge to perform the right move at the right time.

That means, timing is secondary to having better technique. This is after all the best display of high level jiu jitsu. Dominance through tactical and technical mastery that looks effortless. Not a button mashing purple belt. They don't win black belt world's simply by having great timing.

Sure, timing is very important, but skills and skill refinement is paramount. Timing comes from implementing those high level skills and techniques against live opponents. Technique comes from study and practice. Saying that timing is most important is like saying very fast and efficient computer with garbage code completes a task better than a perfectly coded program run on a slightly slower and less efficient computer.

Well, the truth is that technique requirements continue to increase as your level progresses. For yourself, compared to yourself, not based on others. You Will get better if you're studying and training. That does not change at brown and black belt. You absorb technical knowledge and only then are you informed of what to do with it, intuitively or by an instructor, and when. The thing about brown and black belt is that they take the form of belts that require a lot more investment to one's own learning process. People plateau at these belts generally because the spoon feeding of technique slows to a dribble if you're not studying. Why? Because you've learned most of what your instructor teaches. Now it's up to you to gather new techniques and implement them in the right context and refine timing as an afterthought.