Do you really mean two full sets of controls - steering wheel and everything?
A fairly obvious reason for them not being wanted is when the car is used other than for instruction. Brake and clutch dual controls can be locked and/or folded out of the way, and it becomes a normal family car.
I’ve seen specialised vehicles with ‘wrong-side’ (being in a RHD country!) setups, such as ones cleaning roadside drains (basically huge vacuum cleaners), where it makes sense to give the driver the ability to have a clear view of the road edge without mirrors.