No, you don't.
Wars are not won by capturing or occupying cities.
Wars are won by killing or otherwise neutralizing your enemy's warriors.
During the American Civil War, the Union squandered tens of thousands of lives trying to "Capture Richmond" and got nothing for their effort except defeat.
Then came General U.S. Grant who realized that the road to a Union victory was not the capture of Richmond but the destruction of Lee's Army of Northern Virginia. Grant went after Lee's Army like a pitbull and followed it to Peterburg while ignoring Richmond.
When the Army of Northern Virginia was destroyed as a fighting force, both Victory and Richmond fell into Grant's lap like ripe fruit.
During MacArtur's Pacific campaign, the Japanese naval base at Rabaul was supposed to be an impregnable death trap for America with over 200,000 of Japan's finest troops defending it. The Japanese boasted that Rabaul would be the meatgrinder that would bleed the American war effort to death.
MacArthur completely neutralized those 200,000 Japanese troops at Rabaul by simply capturing the surrounding areas, blockading Rabaul and turning Rabaul into the world's largest POW camp without the loss of a single American infantryman. Those 200,000 Japanese troops stayed stranded on Rabaul until the U.S. loaned Japan funds to come and evacuate them several years after World War II had ended.
We do not need to occupy cities in the Sunni Triangle. We do not need to be loved in the Sunni Triangle.
The only thing we need to do is to try our best to isolate the enemy warriors and then neutralize them by either killing them in combat or starving the into submission by classic seige tactics.
That is how wars are won.
The fact that the Baathist die-hards are concentrated in cities in the Sunni Triangle makes their isolation and/or destruction that much easier.