At the end of the day, a postal address is printed to an envelope or package as a single block of text and then read back and parsed somehow by the people delivering the package (usually by a machine most of the way, but even these days more by humans as the package gets closer to the destination). This means that, in a very real sense, the "correct" way to enter an address is into a single giant multi-line text box with the implication that the user must provide whatever is required to be printed onto the mailing label such that a carrier will successfully be able to find them.

Really, then, the reasons why we bother trying to break out an address into multiple parts is not directly caused by the need for an address at all: it is because we 1) might not trust the user to provide for us everything required to make the address valid (assuming the country or even state, or giving us only a street address with no city or postal code... both mistakes that are likely extremely common without a multi-field form), or 2) need to know some subset of the address ourselves and do not trust ourselves to parse back the fuzzy address the same way as the postal service might, either for taxes or to help establish shipping rates.

FWIW, I'd venture to say that #2 is sufficiently common -- as if you need a street address for shipping you are going to need to be careful about sales taxes and VAT, increasingly often even if you aren't located in the state or even country to which the shipment will be made -- that it almost becomes nonsensical to support accepting an address for a location where you aren't already sure of the format convention ahead of time (as that just leads you to only later realizing you failed to collect a tax, will be charged a fortune to ship there, or even that it simply isn't possible to deliver anything to that country)... and like, if you don't intend to ship anything, you actually do not need the full address anyway (credit cards, as an obvious example, don't need or use the full address).