Hachiouji-shi
...why does the 744 uses its Stab tank fuel immediately after its Centre tanks are depleted? ...
If by depleted you meant empty, it doesn't.
The B744 uses the fuel in the stabiliser tank much earlier than that, and starts to transfer fuel from the stabiliser tank, into the CWT, when the CWT contents drop to around 36,500 kg.
I suspect that one reason for the Boeing procedure may be that it is designed to minimise the effect of a total failure of the stabiliser fuel transfer system by detecting any such failure relatively early in the flight.
Given that the worst case scenario of a total failure of the stabiliser tank transfer system can result in around 67,500 kg of fuel becoming unuseable, it would seem better to discover this failure early in the flight, whilst there is still a reasonable amount of fuel in main tanks 1-4, rather than later, when the CWT is empty and the CG likely to go out of limits.
Regards
Bellerophon