On the contrary - if you switch from fully hot to fully cold it takes
*ages* for cool air to start coming through as it's got to remove all the heat from the roasting heater matrix. A cable-controlled flap mixing cold/hot air is far far quicker - the only heat to shift in this instance is that residual in the ducting.If this method of control heat output from a hot/cold input was that good then we'd be seeing it all the time in other uses e.g. mixer taps. The fact is we don't - the KISS principle applies.
Besides which, as discussed, the valve is a common failure point and at £50 a pop from a main dealer it's really something you can do without! You don't hear many complaints from people about their... err.. flaps...
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When going from one extreme to the other, the reason why it takes so long is because of the heat stored in the ventilation system. It absorbs stacks of heat...