[ASipos]

Neither lambda calculus, nor Turing machines "model computation on" recursive functions. Rather, these two, and all the other models of computation are equivalent as they compute the same class of functions from the naturals to the naturals. And we call that class the class of recursive functions.

That being said, a computer is a physical device that is able to compute this entire class of recursive functions. It is what makes it a computer and not a pen or a chair. It's not some esoteric notion. It's the whole thing about it.

[AnimalMuppet]

That's like saying that the basis of computation is the standard model, since all actual physical computers are made out of particles that are in the standard model. It may be true, but it's so far abstracted from what's actually going on that it's not useful at all.