[Yosemite Sam]

I know I look at most things differently from other people but I don't understand anyone's obsession with brakes on a hydro...

If the brakes are engaged before the transmission is disengaged, the transmission will continue to force the tractor in the direction it's moving with the brakes trying to hold it back.

Would probably not really do any damage to the transmission (only because they are so tough) but this isn't a good situation for any part of your tractor, when the brakes start to drag the transmission down this will begin to slow the engine until the governor starts to correct the engine speed... Hard on the brakes, hard on the transmission, hard on the gears, hard on the drive shaft and connections and hard on the engine.

I just don't see anything good coming from this situation.

You would be better off not using the brakes at all.