If you can't define an algorithm as a step-by-step process, what can you define it as? That's the whole point: it is a process, manifested as sets of discrete steps, towards an end result by following sets of rules.

Lambda Calculus, Turing Machines, etc. are no different in this regard. One has its steps realized in reduction and substitution rules, the other has its steps realized in movements of the head and manipulations of the tape.

You'll need more to disprove my hypothesis. All software is built compositionally, up from smaller pieces. It's why we commonly refer to everything as a "software stack": we can reason about smaller making up larger. If you examine most of the code written today, this very minute, you'll see it's compositional, in the way that larger codebases are built from components.

Neither LC or TMs are "natural ways of thought", they're mechanisms. Turns out that TMs won out not only because they admit an easy physical implementation, but also because they're compositional. I can wire up two TMs and get them to perform operations in sequence, perform conditional branching, etc.

JavaScript is hardly Lisp in a C-suit, but that's beside the point, because C is pretty terrible (despite it being my favorite) regardless of what paradigm you choose. I'm not going to devote much of this comment towards that.

All software is compositional, regardless of the medium, and all computation is purely mechanical, regardless of the model of computation, because unless you want to stare at a lambda expression and infer the value, you need to perform some kind of step-wise reduction. That, after all, was Church's point.