You seem to be saying that because we don't
only deal with "statistical systems" we don't
ever or otherwise aren't institutionally or professionally familiar with them.
This is simply not the case.
Your career path may have only ever used deterministic components that you could fully and easily model in your head as such, like assigning to and reading from some particular abstract construct like the variable in your example. I don't really believe this is true for you, but it's what you seem to be letting yourself believe.
But for many of the rest of us, and for the trade as a whole, we already use many tools and interface with many components that are inherently non-determinstic.
Sometimes this non-determinism is itself a program effect, as with generative AI models or chaotic or noisy signal generators. In fact, such components are used in developing generative AI models. They didn't come out of nowhere!
Other times, this non-determinism is from non-software components that we interface with, like sensors or controllers.
Sometimes we combine both into things like random number generators with specific distribution characteristics, which we use to engineer specific solutions like cryptography products.
Regardless, the trade has been collectively been doing it every day for decades longer than anybody on this forum has been alive.
Software engineering is not all token CRUD apps and research notebooks or whatever. We also build cryptography products, firmware for embedded systems, training systems for machine learning, etc -- all of which bring experience with leveraging non-deterministic components as some of the pieces, exactly like we quiet, diligent engineers are already doing with generative AI.