Sorry just found out that adding a field works.
A small thing is that if you add a field to the shipping address only and tick the box shipping address same as billing address it will skip your field even if you set it as required.
Removing or editing the postcode, country and zone doesn't work though, I'm setting up a shop for a local area so I don't need them.
These fields appear in many places: register form, guest form, billing address, shipping address, customer address page. If you would like to modify the source code to remove them, please be carefully.