You could just as easily have said: You can’t subtract large numbers from smaller numbers because that’s not “natural math”. Extending beyond that will not impact “natural math”.
I am pointing out that calling something “arithmetic” in a narrow sense, then declaring that extended concepts can’t be handled within your previous narrow definition is just a tautology of terminology choice.
Yes, a change is a change. And an extension is an extension.
No, that's inaccurate.
Division by zero cannot be defined in a consistent way in the domain that most people talk about it, which is arithmetic.
In other domains, sure, there are useful other definitions of division by zero (as you alluded to in another comment, calculus is one such domain).
But none of those other domains will impact arithmetic, which cannot have a consistent concept of division by zero.