GraphQL doesn't make a ton of sense to me, unless you're expecting many clients with significantly different query pattern requirements and prefer to take on performance and (maybe) security uncertainty & complexity to accommodate that more easily.
If you only expect one client (or a few very similar ones) and you want GraphQL-like division of labor just have your frontend and backend folks actually talk to each other and maybe have the backend folks also write a client library for their services (my preference, most of the time).
[EDIT] but you bet your ass I'm not putting up much of a fight against it if I'm in anything lower than a development lead or architect position—no use fighting that fight from poor footing when, as you mention, it's +5 CV points anyway, so who cares if it's maybe not the best solution :-)