I can only relate my experience.
I believe my car was SLIGHTLY faster using the brake, compared to foot braking. . M y personal benefit of the brake was more consistent lights. Stepping off a button was easier than swapping feet. I didn't use a two step, just wooded the throttle at the first yellow, stepped off at the third. 5300 rpm leave.
But that transbrake leave was FUN! Small wheelstand with the brake, left flat footbraked.
My memory may be faulty, but I'm pretty sure deep stage was not allowed in super pro, our only pro tree class. Exactly why I ran pro. Full tree, no box!