Well, you raise an interesting point, Col.
In principle, TCS works best when all diffs (centre included) are *unlocked*. In an ideal TC system, the brakes should be applied independently to each wheel, and progressively. With all open diffs, only one wheel will spin when traction is lost. The ideal TCS would progressively retard that wheel to the point where next wheel will also start to spin (or of course, the vehicle moves forward). TCS will then progressively apply the brake to that new spinning wheel, starting at low pressure,
while still maintaining the higher pressure on the first wheel. And so on, until all four wheels are turning. This all happens in an instant, and can be repeated several times per second.
This ideal system would minimize the total amount of braking force applied, so maximizing the useful engine power, and minimizing brake wear.
Any locked diff would potentially mean that the TCS is trying to stop a wheel from turning when it
has to turn. For example, with the rear and centre diff lcoked, and good traction only under one front wheel, a TCS would try to hold the rear wheels, until the front wheel with grip started to turn. But the transmission
must turn the rear wheels if rear and centre diffs are locked.
(In practice, TCSs tend to substitute independently progressive braking with a series of momentary "grabs" at a wheel. The frequency of these grabs does much the same thing as progressive braking, but a bit more sloppily. A system with independent braking pressures at each wheel would be hugely complex, I imagine. But the overall effect of the simpler system is very similar to what I described.)
Locking
all the diffs avoids any problems - the TCS isn't activated, because all the wheels are turning. Locking only the centre diff makes TCS a little less efficient, but seldom creates a serious tussle between brakes and transmission. And the benefits of locking the centre diff almost certainly outweigh the disadvantages.
I'm not a big fan of TCS. It has two advantages - it's pretty much idiot-proof, and it's very cheap to add to an ABS system, as all almost all the hardware is there already.
But it can sap a
huge amount of power (contributing to overheating if the car's already working hard in hot weather), it wears out your brakes, and even the fastest system are reactive - a wheel has to stop before TCS kicks in.
Actually, I can't see the point of anything other than a full manual locker
Rgds,
Michael...