Apple also does it via “hide my email”.

But that's just an identifier which you can easily update when you move, like a domain=>IP mapping? Businesses still have your physical address.

A system where they didn't get our address at all would be great but I think we would also need alternative payment providers that don't share any billing-related address information with the business.

I love this idea, but then doesn’t it create a centralized target for hackers?

I suppose that’s still better cuz then it also creates a centralized point and resources for securing the database.