Yeah the Ambruzzi glide I have in the 69 came with a protree brake that requires you to activate the transbrake to back up, I couldn't tell you why other than it's a protree brake and every one that I've seen operates that way.
Now to answer your other question I'm a die hard footbraker, and the class doesn't allow you to leave off a brake, not that some people aren't leaving off them, but that's another story.
I have left off a brake a few times in Landon's Nova, mostly on nitrous passes after the races or just messing around trying something different.
Have a good one, Cp