I've come to the conclusion that executability and reasoning are separate axes. If we view everything in terms of languages with interpreters, of course functional semantics must be executed by imperative machines. But to reason about either kind of program, we need functional semantics, because functional programming is the language of pure reasoning.
But folks have reasoned about imperative things for a long time, as well? It is certainly easier for many analytics to get into a functional form. But would be a stretch to say it is always easier. Fractals are often my go to example where imperative is easier for many constructs.
I view it like coordinate systems. Polar versus Cartesian coordinates can clearly both do the same things. They each have domains where they have advantages.
You could argue that time based logic systems are the end goal, maybe? Still feels like throwing babies in bathwater.
Edit: for a fun example of reasoning without programming "functional" logic, look up juggling diagrams/notation. Not all logic is symbolic in the same way.
This doesn't feel in contrast to what I was saying. You can reason about imperative code, but you have to add things to it to reason about it, most importantly the notion of a memory store. This is because imperative code assumes an underlying CPU + RAM which holds state.
It's not that it's easier, it's that imperative code has implicit state.
Fair that I don't intend my question there as a full rebuttal. I do question if functional semantics are fully needed any more so than other tools. In particular, I recall formal methods was more about prepositional logic than it was functional semantics.
And yes, you have to add and remove things to any model to really be able to reason about it. Is why engineering dynamics is harder than engineering statics. Things that change are hard. Reducing this to state being the enemy, though, I think is wrong in a lot of functional advocacy. State can be reasoned about without having to boil the ocean, as it were.
More on the subject: https://concerningquality.com/quality-and-paradigm/