This is the most complete and factual analysis I have seen on Slashdot so far. What concerns me and would stop me from embracing the strategy we have chosen were I sitting in the oval office is, that "the enemy of my enemy is my friend" does not hold up after the original enemy is gone.
Al Qaeda and its offshoots and subgroups in particular are propaganda machines. When Daesh is defeated if it ever is, we will again be the Great Satin and just like before I suspect we find ourselves faced with the training and likely weapons we have provided turned on us. Its how these leaders hold on to power. Personally I think out best bet would be to just disengage form the middle east. let Southern Europe, Russia, China, Israel and the more stable elements in North Africa contain it if they can. While politically sacrificing Iraq and Afghanistan at this point is a tough pill to swallow, in the most mercenary sense the potential payback from stabilizing those places in no way approaches the costs.
Daesh could be very useful to us in that if we left it unchecked it will likely put a great deal of strain on Iran, Russia, and eventually China will be drawn in. These are our economic rivals, its hard to imagine we don't gain from them being in a multi-trillion dollar quagmire we have been stuck in for fifteen years now. A few decades of not seeing American's dropping bombs over there might cause a refocus of some of the extra-regional terrorism objectives as well.
Personally I think our best move is to pack up and go home. No foreign aide to the region. State department imposed travel bans for Americans. Lets just watch from the satellites and see how it pans out.