WWV/B/H is definitely a critical service, since there are things (industrial devices and such) that rely on its presence in order to function properly. As is the NOAA weather broadcasting service, which is also presently still on the air. (Well, KIG98 is, anyways.)
As far as I know, WWV/B/H is not part of the Broadcast Board of Governors, being a unit of NBS/NIST instead. The BBG services (VOA/RFE/RL/Sawa etc.) are most certainly *not* "critical" services by comparison.