Arguments from mathematical or physical theories or axioms miss the point.
When writing code we need to understand how our code will behave over it's possible inputs. There's nothing inherently wrong with deciding that in a particular bit of code you're going to ensure that "dividing" by 0 gives you 0 (for example), as long as you know what the consequences are for the behaviour of the programs relying on this.
The reason mathematicians get upset by this is that this is not what is normally understood by division. Division by zero isn't defined. Whatever we do in our programs isn't going to change that