The clear strategic objective is, as it was in 2003, to prevent the control of national assets to fall into the hands of violent militants who will use them against Americans. As before, those national assets may or may not include chemical and nuclear weapons at the moment, but in time they will. I stated then that the best we might expect out of Bush's intervention was to buy us time, rather more time, I hoped, than we actually got courtesy of his successor's malign and incompetent meddling. But the strategic situation has changed since then. A threat to the Saudi wells is no longer an existential threat to the world economy; it's a dangerous one, to be sure, but not what we faced in '03 and definitely not what we faced in '91. That changes what ISIS can and cannot do despite all the chest-pounding about smuggling nukes into New York. That's fluff for the cameras; they're not ready for that yet because they're not ready to follow it up. In time they may be.
On the other side of this coin, if we take ground we're going to have to hold it, because the Iraqis don't seem to want to. Nor, actually, does any sober American strategist. What Bush found out was that yes, you can build a nation if you're prepared to prop it up indefinitely. If not, not.
In the north we have the Kurds who have proven that they can both take and hold territory, but at whom the Turks look at askance because they claim what the Turks call their own. That is a diplomatic challenge, not a military one. In the east, the Iranians who are having the usual ethnic and sectarian problems moving west. Nuclear weapons won't help that. In the south, the Saudis will be nuclear themselves very soon if they aren't already. In the far west, we have incessant warfare from the Golan Heights to Yemen.
What we do not have is either the means or the determination to straighten this mess out, if that is even possible. Five millennia of recorded history suggest that it might not be. My humble suggestion is for us to do what we have the means to succeed at: strengthen the periphery in Israel, Egypt, Jordan, and Turkey should that country decide it prefers to be part of the solution instead of, as at present, part of the problem. I wouldn't bet on the latter. As for the rest, I don't think you can really stop people from fighting who want to.
We were typing at the same time...you are the better writer.