Is there any particular reason the A380 doesn't have a centre wing tank?
It simply doesn't need one. Depending on the source, the A380 has a range from 8200 NM1 to 8477 NM2. The current longest scheduled flight is AKL-DOH, which is 7848 NM3. So the current configuration is capable of flying any of the current routes. 

As far as the A380F, it really wouldn't make sense to add a center tank there either. The extra fuel weight would mean less cargo capacity available.

 1 Wikipedia

 2 Aerospace Technology, 11/19/2013

 3 Wikipedia