Perhaps you could explain why this matters. What can't we do with our math that we could do if your fixes were implemented?

I disagree with the "special rule" analysis. Adding or subtracting zero is just a linguistic code for doing nothing. Multiplying by zero is just a way of saying that we have nothing; three twos are six, zero twos are nothing. Division by zero is "undefined" in the way division by a tuna hoagie is undefined. Zero simply is not a valid input into the division algorithm. There is no reason it should be. The purpose of the algorithm is not served by using anything other than a non-zero number as a divisor. ANYTHING that is not a non-zero divisor is disqualified. So, zero is disqualified. No big deal, really. Nor is there any reason that every "number" have all of the same qualities as any other number. Six can be factored, and seven cannot. Six can be a divisor, and zero cannot. Life goes on.

I did like the monkey story, though. It shows how the wisdom of tradition is implemented. So long as a monkey reaching the banana would trigger an ice bath, the tradition "works," even if ostracism is the punishment for attempting to violate it. What happens when the ice bath regime ends but no one knows it has ended? That's where a lot of social strife comes from. But it's got nothing to do with math.