You don't want to wear a headset just for the mic, but have the caller's audio come through the speakers. So, you can either have that audio go to the computer speaker or to the headset.
The Flash configuration pop-up only lets you choose your mic, but not your speaker. To use the audio through the browser, the notification 'ring' AND the audio from the caller goes to the Windows default speaker. Our support people don't have their headsets on all of the time and are often flipping between applications - meaning they don't always have Zendesk on-screen.