JustAFan
The Adebayo Akinfenwa of football photoshoppers
As Euron put quite succinctly to Jaime in the last episode, "They just love severed heads really." The people of King's Landing will follow basically anyone holding the crown out of fear of punishment, out of blood lust, out of adoration - basically out of anything except actual loyalty. They revolted once when Joffrey was king and the food supplies were low due to the war. Margaery soon tempered that anger and once the war was over food returned to the streets. Not that the show will focus on it because we're past the point of politics really meaning anything to this story, but Cersei can now use the fertile lands of The Reach to flood the capital with food again and regain some actual popularity as opposed to ruling out of fear that she could just press the button again.
I think the fear thing is pretty big. The masses were pretty willing to follow the High Sparrow and hate Cersei when given the chance. But after the whole nuking of the sept, well it might be they are feeling a bit cowed right now. Plus with news of a new Targ on the continent with DRAGONS and Dothraki and Unsullied, they also might be taking the certainty of what they know Cersei is over the unknown (and thus fear) of what these newcomers to Westeros might do to them all. ANd as you say I she can free up a lot of food for those in KL then she will be supported by them for now.