I'm not sure if it's been made clear as to how you've determined that the AWD distribution to the front axle is not functioning. (This is not to say that it isn't...it just hasn't been made clear in what I've read so far).
Just to be clear...the early e53 X5 doesn't have xDrive...the 2000-03 models have an AWD version that is similar to early versions of BMWs used a decade before but with the addition of DSC. It is referred (rarely) as DSC-X. This DSC-X AWD/traction control system was replaced with xDrive starting with the 2004 X5 model year.
See the info below that explains this pre xDrive AWD systems...and take note of the information about ADB (automatic differential brake)...where ABS braking is applied to the front axle (if wheel slip is detected) and allows the rear axle to slip/spin: