And you can listen to your favorite radio station only because the Federal Communications Commission brings organization and coherence to our vast telecommunications system.
Time standards that were adequate to their day were around before NIST. NIST has done an awful lot of bad things, too. (Or tried to... remember the Clipper Chip?... oh, and there was that recent thing about encryption standards...)
AM and FM radio haven't been a significant part of our actual "telecommunication system" since maybe 1960. Other than the occasional storm warning.
I think you misunderstand the post. Radio is definitely a government thing and the most important thing the government does in this field is frequency allocation. It's vital for modern society.
Without frequency allocation anyone could broadcast at any power at any frequency. Just think about that and how much is still controlled via radio/microwave signals. The following things rely on there being set frequency bands with no outside interference:
Public radio and television
Air traffic control and air-air communication: only one person can talk at a time, one idiot transmitting by mistake can jam the channel.
Anything at 2.4GHz
900MHz short/mid range signals e.g. Zigbee
GPS and other satellite uplinks
Radio time signals
Astronomical bands of interest (e.g. 21cm)
Military, police and emergency service bands
There is no way this would happen without a government, you need someone to put their foot down and organise the spectrum so that everyone can operate without contention.