I do have a front-end, but it interacts with the server with a specific, private API. It's using a more compact data encoding than JSON optimised for streaming the data that's needed for the front-end.

But yes I agree with your point: for a simpler app with a more traditional web UI it's likely the API used by the front-end would largely overlap with the user-oriented API. Then indeed the REST API has to be maintained for as long as humans continue to use the front-end.