"This box thing appears here. It should have X Y Z info from the object" which was born from "Let our customers know about the new object".
Aren't you going to see a lot of the same requirements from projects as a consultant? If so, then you're just implementing something you've already done before, +/- some unique features. So if you're something like a 10x consultant or a $200/hr consultant, are you doing that because you're dealing with new problems constantly? I'm a little less impressed if someone can command that rate and has done 20-30-50+ projects in the past that are mostly the same thing. That's just paying for experience.
Nobody is doing that AFAICT, it's just why being a consultant is different from having a job.
"Aren't you going to see a lot of the same requirements from projects as a consultant? <snip> That's just paying for experience."
Well sure. It's the experience and the domain knowledge that makes that somebody can do something at a higher speed than someone else, and that somebody knows what a customer is looking for without them having to spell it all out. I'm nobody special, and I'm certainly not claiming that I'm a '10x consultant' in the sense that I'm 10x better than the average or whatever. I was just reflecting on the underlying mis-assumptions in the GP's question.
Also, it's not because somebody bills 200/hour that they make 2004050 per year. Jobs are not like doing consulting. I'm doing OK, but (after discounting for everything) I'm making roughly what a senior employee would. Some do better, again I'm not claiming I'm anything special (and I guess I shouldn't have made this about me by mentioning an example from my own work) but some of the 'calculations' I've seen in this thread are nonsense. It's like people saying 'Mohammed Ali made x million per second in his fights'. Uh, sure.
Product manager is an imperfect solution to a problem your customer doesn't care about any more than he cares about the name of the obscure sorting algorithm you used to scale his system 1000x.
Really, everybody reading this (yes also those in the UK!), if you are an experienced or senior software engineer and you're billing yourself out at these rates ($1000 a day), you're leaving money on the table. If the mentioned work is what I consider 'data science' (i.e., advanced applied statistics requiring fair amounts of high-end, performant software engineering), then $1000/day is really low if it's for anything more than what somebody can do as a weekend gig next to their day job.
"How exactly does the developer do that, without extensive consultation time with the client?"
Well yes you answer your question yourself - top 10% rates are for those who can make the customer happy with the result without having to drag exact specifications, kicking and screaming, from somebody who doesn't want to deal with all those details.
(also, here is the first hint: somebody who thinks about '200$/hour' has the wrong mentality. I do projects where my rate is that, but I never ever (ever) put it that way. Sell services based on benefits or value for the customer, not on how many hours you're going to spend. Nobody cares whether you've spend 6 weeks working 100 hours a week, or if you send 5 emails with the right words to a few people and wrote 100 lines of software on a lazy sunday afternoon. Effort: irrelevant, make customer happy: only thing that matters.)