In case of a complete redesign, yes you're right. With a generic API you will have about as much trouble writing the redesign as you did the original design.
In practice, a complete redesign is an incredibly rare event, and a good problem to have. Usually design of individual pages and layouts undergoes gradual, incremental changes, driven by real needs.
A redesign that requires front-end restructuring to such an extent that the data supplied is no longer sufficient should probably involve backend collaboration. Otherwise, you're tasking your backend team with building a generic site builder, which is much harder than a specific backend for your frontend.
In practice, a complete redesign is an incredibly rare event, and a good problem to have. Usually design of individual pages and layouts undergoes gradual, incremental changes, driven by real needs.
A redesign that requires front-end restructuring to such an extent that the data supplied is no longer sufficient should probably involve backend collaboration. Otherwise, you're tasking your backend team with building a generic site builder, which is much harder than a specific backend for your frontend.