Why is the text-to-speech hotkey not working?
I have found a solution that worked for me without restarting (although restarting worked before when this happened)

My problem was that both the Hot Key or the contextual menu Right-Click -> Speech -> Start Speaking did not work within any application like Chrome and Text Edit

When I went to System Preferences -> Accessibility -> Speech -> Play the button toggled to Stop as if playing but I heard no audio.

My Solution: I switched my default voice from Heather Infovox iVox HQ to Samantha then pressed the Play button. 

I got audio. 

Then I switched back to Heather and both Hot Key and contextual menu Right-Click -> Speech -> Start Speaking worked without quitting any apps or restarting my computer.