There are certain limitations on what makes a compound suitable for use in a drug. Other scientists have already approached the problem from that end, creating designer molecules (billions of them) and filtering out the ones that don't have "drug-like" properties. This process rapidly gets too technical for me to understand, so I'll not confuse you with details.

Most of these massive libraries are also constructed in a way that means all the compounds can actually be synthesized using existing techniques, so can be used for further testing immediately.

So, MPCevat, while there are other strategies for finding drugs, other research labs around the world are already exploring these possibilities.

As for a common denominator - it is my understanding that the complexity of the bond and the number of different ways a drug can bond to a protein means that backtracking is considerably tougher than it sounds - and currently simply isn't practical (and due to these factors, there is no obvious common factor in the drugs that are already known). Besides, one of the goals of FAAH is to find drugs that are effective against many mutated forms of HIV.