The FCC exists (in part) to enforce a certain morality on public broadcasters. Whatever we think about that today, that was a core responsibility of the FCC when it started and that still exists today.
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As a separate matter, it's long been clear the FCC was created to serve a very time, context and needs - most of which either no longer exist or have changed substantially. Most media no longer travels through the limited shared resource of "airwaves". The agency's whole charter is in need of a major rethink.
Your next point about the FCC needing a major rethink is interesting. What are you thinking here? FCC also regulates internet-based communications (e.g. Youtube or podcasts)?