Can't chip-making machines be made without chips? Yes. The very first one, at least, was made like that.
My understanding is that as you design more powerful chips you use those chips to design more and more powerful chips.
Some older 8bit cpus now have kits where you can make them from components (20x slower and many times larger…)
Walking into a corn fed post-apocalyptic future knowing that soaking your corn in ash water and hulling it prevents pellagra and improves the viability of your group is some handy knowledge.
This is also why rebuilding a web page after deleting it is so much faster the second time around. You've solved problems on the first go round that weren't apparent when you started.
I think this means we should keep log-books like ship-captains do so we can avoid treacherous waters on subsequent trips.
Counter-intuitively though, while a lot of people think rebuilding software from scratch will be a lot faster, in practice it's not because people tend to have to re-invent and re-discover a lot of things, and bolt a lot of other stuff on top as well. Plus over-engineering, plus analysis paralysis, etc.
So making a carbon copy of e.g. a website: sure, but for a lot of software it doesn't work like that.
That said, I do believe rebuilding software will work out better in the long run because learning from the mistakes of the past. It'll be interesting to see what e.g. Google's Fuchsia will turn out to be, the first big / sponsored OS made from scratch in a while.
And Firefox / Rust is another interesting one; it was a massive investment and risk, but I think it's paying off.
It's not crazy that a complicated bit of machinery has a few thousand individual chips in each one.