Why is inhibition of inhibition (reciprocal inhibition) such a common motif in cell signalling?
This feels like a my philosophical question...

Direct regulation of proteins would have to have biological utility - such a gene has to be driven by positive selection to adapt that ability.  The question is more about learning what might be driving its role. 

I would hazard that protein deactivation and degradation would be important to make sure that these inhibitors could be down-regulated fast enough - if they were left to degrade via a general pathway, the specific signal would not be available for too long a time.