BEIRUT—In the three-way war ravaging Syria, should the local al Qaeda branch be seen as the lesser evil to be wooed rather than bombed?

This is increasingly the view of some of America’s regional allies and even some Western officials. In a war now in its fifth year, in which 230,000 people have been killed and another 7.6 million uprooted, few good options remain for how to tackle the crisis.

The...