When braking, there is a lot of down force on the tail end of the transmission, when the drive train incorporates a torque tube.
When braking, there is a almost zero down force on the tail end of the transmission, when the drive train incorporates a Hotchkiss or open drive.

So I would say that the 47-53 truck rear-transmission frame cross-member is not needed when the drive train incorporates a Hotchkiss or open drive.
That said extra support does not hurt anything.
The rear-transmission frame cross-member might aid in preventing the frame from twisting.

Because of the design of the 47-53 rear engine mount cross member.
The engine & tranny weight want to pull the frame rails inward.
Hence the need for a rear-transmission frame cross-member.

GM redesigned the Rear Engine mount cross member in 1954 hence no need for a rear-transmission frame cross-member for trucks equipped with manual transmissions..