What might happen is the rise of an informal communications channel managed by employees that Google executives cannot direct let alone cancel. That's far worse in a way.
Communication implies two sides. If one is not willing to listen, what's more likely to happen is instead of communication channel an echo chamber will form and without the avenue to vent frustrations the rhetoric will get more and more extreme as people assume the worst, often incorrectly.
A communications channel controlled by the workers and not the managerial structure? This is a truly tragic development.
The issue of "control" is pretty peripheral to this conversation. TGIF was a fixture in the company culture and as such nobody really "controlled" it. It was just expected that it'd happen every week, you'd go grab a beer, and watch the execs answer the top voted Dory questions they'd rather avoid, at least from time to time. That was a crucial feedback mechanism which is now at least reduced if not gone entirely. This will make the system (Google) less stable.