> There are obvious difficulties here regarding how we'd handle certain fields (e.g. how do I calculate your shipping if I don't know your exact zip code)
Forget calculating shipping; how do you ship me my product at all without me giving you my address?
(A quick napkin sketch would be that I wouldn't, I'd give you a USPS reference number, which you could use to calculate shipping costs as well as actually mail me a thing; only the USPS would be able to link the reference number to my physical location. There's almost certainly problems with this idea, which is why it's a napkin sketch.)
Forget calculating shipping; how do you ship me my product at all without me giving you my address?
(A quick napkin sketch would be that I wouldn't, I'd give you a USPS reference number, which you could use to calculate shipping costs as well as actually mail me a thing; only the USPS would be able to link the reference number to my physical location. There's almost certainly problems with this idea, which is why it's a napkin sketch.)