I think much of modern PL research (and with a little poetic license, all of the original PL research) is actually dedicated to developing PLs as human language

I think much of modern PL research (and with a little poetic license, all of the original PL research) is actually dedicated to developing PLs as human languages for expressing pure, true thoughts. What is "pure and true" in this context? That was the question which originally drove the invention of PLs or logical languages and answers were attempted near the beginning of the 20th century by Russell, Whitehead, Frege, and many others. Church, Curry, and Turing, notable names in early CS, were actually largely driven by Hilbert's mathematical program of formalizing mathematical logic. So what does this effort look like today? PLs of this pedigree are barely at all interested in how binary codes work (unless they are the object of study, of course). Instead, they endeavor to provide valid logical frameworks of massive expressive power. Modern PLs in this vein can formalize mathematical logic through intuitionistic logic which is something like the logic most people learned in school but augmented with a notion of the limits of the Halting Problem. This means that it lives nicely between logic and computer science. So why do we think that PLs are an object of computer commands? Because the popular ones which were both widely implemented and fast had that property. It's essentially a walk in the park to convert Assembly to machine instructions compared to an intuitionistic logic calculus. We then proceeded not by seeking to make Assembly more like its forebearing languages but instead to layer abstraction after abstraction atop it to make the fundamentally alien task at hand more manageable. This is ultimately a flawed program judged that way. Furthermore, it's also less than half as old as the original PL research efforts, but it already had us develop many techniques for efficiently executing complex tasks on a computer. This is an important part of "computer algorithm design" but essentially a side-topic to the larger field of PL research.