I'm surprised it hasn't been common practice.  I would assume the conversations in the West Wing are sensitive,  often classified or close enough to classified to treat as such.  It's common practice in government, at least DoD, facilities to have lock boxes outside of offices or meeting rooms. 

Heck, I've made meetings classified just to keep out the phones of a couple mad texters, who routinely reported too much back to their patrons.  It's an easy OpSec fix.  :-)