There are a few possibilities:

• It's faster, especially if the handbrake isn't applied already.
• Some cars, like the one I drove most of the time in driving school, have an automation to keep braking for a second, so one just needs to: Brake, Clutch, Put in gear, Release Brake, Rev up engine a bit, Release Clutch.
• My current car's Handbrake is basically non-functional, so I have to do the fast foot shuffle.