One thing abt going for fast lens is not just because you can get more shutter speed, many people dun realise that the variable aperture is a PITA, everytime when you zoom in and out.
Take the 70-300 for example, think it goes from f4 to 5.6. Sure you can overcome this by stopping down to f5.6, so when you zoom out, it will stay at f5.6. But in this way, you are losing 1 stop of light from f4.0.
For fast pace stuffs, you really want the aperture to stay constant hence not affecting the exposure, so you can concentrate on the framing and composition of the photo.