This assumes very slow AI progress. I'm not one to hype up LLMs, but I would never claim it'll take 200 years before an AI can untangle a sewing machine with robot hands. Stuffing an envelope and applying a stamp? My bet is less than 20 years. That's a level of tactility that can do a tremendous amount of real-world activity. And the capability of a high end robot controlled by a human keeps expanding, so in the hypothetical "AGI" scenario the flood fill gets pretty big.
Self-driving looks like a much easier problem, it has gotten a massive amount of investment in the last decade, and it's not fully solved yet. Compared to that your 20 years estimate sounds way too optimistic.
I guess it's time to bring up "Why today's humanoids won't learn dexterity":
https://news.ycombinator.com/item?id=45392922