The arguement I have read is that the device the president had was only possible because he has a full security detail 24x7 that can keep track of the phone. Doesn't the secretary of state have that as well?
That's the real paranoia. What if the black phone turned into a wireless bug? Anything wireless inside of a SCIF is "bad." The black phone is just an exception for national security reasons, the default is to deny all.