Formal logic is a tool used by computing scientists and that they made almost incredible contributions to. It’s a tool that’s available to other scientists too, and the more rigorously minded ones use it.

For your latter point, it’s a matter of elegance, which is a pretty way of saying cognitively manageable. Think of epicycles vs Newtonian mechanics as an analogy. With enough epicycles you can compute the same result, but Newton’s approach is still a clear scientific advance.

Your point about design is well taken. Any given design is analogous to a theory. So we should aim for the simplest and most cognitively manageable design that satisfies our needs. That’s not literally formalized, but it’s a well established principle with an excellent record.