I've written up three different replies now and I don't like any of them. I'm not sure how to respond to this statement. Thank you for writing it.
I fundamentally disagree with the two assertions "it's the act of using your brain to simulate the computer that teaches your brain how the computer works so you can reason about it later" and "In most domains, I find it best to start with doing things yourself, and only move on to the tool-assisted version once you thoroughly understand what the tool is doing for you".
I agree entirely with the notion that ability to reason about the underlying system is incredibly important, but I disagree about the methods to get there.
I disagree with those two ideas because (and maybe we have different perspectives here) but the choice of whatever level is the "base level" or "bottom of the stack" seems entirely arbitrary every time. Is assembly the bottom? Or C? No it's machine code. No it's the physical wires.
I think I should come back to my original comment here and reiterate. I'll clarify what I mean about those "computing environments that do that thinking for us" because I expressed myself poorly.
There are computing environments and workflows that people have built which expose to the end user (the programmer) deep information about the state in which they are working. As a field, as a culture we have not embraced this thinking and rather stick to the simplistic notion of working alone to build understanding for ourselves alone.
Sharing is discouraged (outright banned at school under penalty of expulsion) and difficult requirements are kept in place primarily for hazing purposes rather than pedagogical(I have this from a one-on-one discussion with the course designer at my school). There's this thinking that "I had to go through it, and the system produced me, so it must be good" and to think otherwise would be a recognition of being failed by the system, of missing something. A recognition that you could be smarter now than you currently are.
So to give a concrete example, as my sibling comment talks about "being the packet". Why is the 'network', and 'understanding the network' not realized as exactly the same idea? Why should I ever have the simulate the network in my head? The network is an man-created artifact, my understanding of the network should come from the network, the literal code defining it, not from text file RFCs however well they are written and whatever brilliant ascii art they have (because they ARE well written, and well explained by their diagrams). Programmers should have inspection tools that are borne out of the definition of the artifact they are inspecting.
This is of course being done in other disciplines first. An architect working in Revit is orders of magnitude more powerful than an architect working on pen in paper. In every case where an architect prefers pen on paper it is due to a failure of technology to realize practical or targeted workflow affordances, not due to the superiority of paper.