Burrard Bridge is not the only bridge heading into downtown Vancouver. Granville St bridge heads into downtown and is underutilized. Many of the drivers can use that bridge instead of Burrrard. I have driven to the downtown core for many years using both bridges and I have had no problems with cyclists.
I do know for sure that at 5:15 the burrard bridge is heavy with traffic. Maybe that live webcam was taken on a holiday? Don't know, but I've never seen the Burrard bridge at with barely any traffic at that time of day.