The problem is that this is really only possible with a toy model of a computer and very simple programs. Modern chips with their branch prediction and caching and threading and advanced vectorized operations and so on are vastly more complex. The 6502[2] was perhaps the last chip that one person could fully grok. Maybe a chip designer at Intel or AMD could understand the whole circuit in detail but no one else has the time - it would literally be a full time job. The same thing is true for operating systems - even if you're Raymond Chen, you can know a lot about Windows, but you can't know everything.
We learn just enough about the other parts of the system to convince ourselves that we understand the principles. We build the basic mental model we need to interact with other systems but all we can really do focus on our own specialized areas and hope that everyone else is doing their job. This works well enough until something like Spectre[3] or Meltdown[4] crops up and that's when we realize that we've been building castles in the sand.
[1]: https://www.nand2tetris.org/
[2]: https://en.wikipedia.org/wiki/MOS_Technology_6502
[3]: https://en.wikipedia.org/wiki/Spectre_(security_vulnerabilit...
[4]: https://en.wikipedia.org/wiki/Meltdown_(security_vulnerabili...
We really depend on three things - knowledge (stored collectively and in various media eg books), materials (tools and manufactured precursor goods, available via active supply chains or existing stores), and most importantly having our basic needs met trivially so that all our time is not sucked up addressing them.
A scenario where someone has a 'wasteland' to pick over for their basic needs, knowledge and materials looks quite different to a return to primitive living where what nature provides is all their is to work with. 'if you want to bake an apple pie, first you must invent the universe' or however it goes...
Then of course there's the question of why someone would have any interest in obtaining computing power were either of those scenarios to occur. Much like the 'how do we warn future civilisations about our nuclear waste' problem perhaps it is acceptable to not bother, they'll figure it out again on their own eventually given enough time.
This stuff is fun to think about at 6am when hay fever is preventing my sleep :)
Knowing how it works, and being able to build a new one, are also two very different problems. For example, there are plenty of Computer Science folks who learned how to design chips (layout the circuits, write the microcode, etc) - but you need a whole extra background in EE and Physics to be able to fab said chip...