I'm not disagreeing with your comments but put yourself in the loaded pairs position. (Unloaded on cross-straps shouldn't be a problem). Imagine meeting another boat at a bridgehole, the other boat should be able to stop very quickly, a loaded motor takes far longer. The loaded butty carries on regardless, stuffing it in the bank may not be an option due to moored boats, even if you could the result may mean an age trying to refloat it again afterwards. The motor steerer meanwhile has to throw the motor in reverse, try to steer, quickly pull in yards of tow line so that it doesn't foul the prop', worry about where the butty is going - all of this in the space of a few seconds. If the butty steerer doesn't manage to hit the motor square up the arse of the stern fenders (this is difficult to achieve) then the butty flies past the stern of the motor and all hell breaks loose. Nobody will be going anywhere for a while.
Consider the same situation except that the other boat stops, loaded pair go through the bridge, then other boat goes through - no problem. Surely this is the far better and stress free scenario.