The presence of a separate, non-computational storage in computers based on the von Neumann architecture implies the representation of state (at some level or another) is possible by those same machines. Consequently, we are tempted to utilize that capacity for state as storage for intermediate data within program execution itself, rather than just as a place to store the executed program itself.
I could be totally missing the mark on it having to do with the von Neumann model of storing, fetching and executing programs. But from my limited reading about computers such as ENIAC, which required the circuit to be altered to route signals prior to execution, and then run through the program all at once. Someone please correct me if I'm wrong, because this stuff fascinates me and I'd love to be told straight.
TL;DR: Storage implies state, so we wrote tools (languages) to leverage that.
But there is that step of translation. Perhaps we became so fluent that we stopped noticing we were doing it, and perhaps even to start thinking imperatively. But it's not "natural".
Look at computing polynomials by differences (giving rise to the idea of the difference engine): better described as an iterated procedure than an imperative program.
Or "constuctive": Construct an ellipse naturally by the pins and string method. Bisect an angle naturally using straight-edge and compass.