How quickly could robots scale up?

I'd be interested in an attempt to zoom in specifically on the "repurpose existing factories to make robots" part of the story. You point to WW2 car companies turning into tank and plane factories, and then say maybe a billion humanoid robots per year within 5 years of the conversion.

My wild guesses:

Human-only world: Assume it's like ww2 all over again except for some reason everyone thinks humanoid robots are the main key to victory:

Then yeah, WW2 seems like the right comparison here. Brief google and look at some data makes me think maybe combat airplane production scaled up by an OOM in 1-2 years early on, and then tapered off to more like a doubling every year. I think what this means is that we should expect something like an OOM/year of increase in humanoid robot production in this scenario, for a couple years? So, from 10,000/yr (assuming it starts today) to a billion/yr 5 years later?

ASI-powered world: Assume ASIs are overseeing and directing the whole process + government is waiving red tape etc. (perhaps because ASI has convinced them it's a good idea):

So obviously things will go significantly faster with ASI in charge and involved at every level. The question is how much faster. Some thoughts:

• ASI probably needs far less on-the-job experience than human companies do, to reach the same level of know-how. Like, maybe if you let it ingest all the data from Tesla, Boston Dynamics, Ford, GM, SpaceX, etc. collected over the past two decades, and analyze all that data etc., and if you give it the blueprints and prototypes for the current humanoid robots, it can in a week spit out a blueprint and plan for how to refit existing factories to produce mildly-improved versions of said robots at a run rate of about a million/yr, the plan taking six months to execute on in practice. (So this would mean 2 OOMs in 6 months whereas in the human-only world I was guessing 1 OOM in a year.)
• Think about how much faster Elon & his companies seem to be able to get things done compared to various legacy companies, and extrapolate -- seems fair to assume that ASI would be at least as far above Elon as Elon is above typical competitor companies. Probably in fact that's a super conservative assumption. "But muh bottlenecks" --> "The whole point is we are trying to estimate how harshly the bottlenecks bite. They evidently don't bite harshly enough to stop SpaceX from seemingly going like 5x faster than Blue Origin." Also, Elon is only one guy, and his companies have a limited number of employees thinking, at human speed who can't just copy themselves like ASI could.
• There's also 'sci-fi' stuff to consider like nanobots etc. I think this should be taken seriously, much more seriously than people outside MIRI seem to take it. I think we basically don't have a way to upper bound how fast things could go post-ASI, or rather, I think the upper bound looks like Yudkowsky's bathtub nanotech story. 

Overall I'd guess that we would get to a billion/yr humanoid robot production within about a year of ASI, and that the bulk of these robots would be substantially more sophisticated as well compared to present-day robots. And it's easier for me to imagine things going faster than that, than slower, though perhaps I should also account for various biases that push in the other direction. For now I'll just hand-wave and hope it cancels out.

On one side: Humanoid robots have much more density of parts requiring more machine-time than cars, probably slowing things a bunch.

On the other, you mention assuming no speed up due to the robots building robot factories, but this seems like the dominant factor in the growth. Your numbers excluding that are going to be way underestimating things pretty quickly without that. I'd be interested in what those numbers look like assuming reasonable guesses about robot workforce being part of a feedback cycle.