Local density bubbles would have "popped" or decreased in size during inflation, making their curvature less noticeable.
Inflation would have heated up and thus smoothed out any local variations in curvature.
Rapid expansion of the observable universe would have crushed any local variations in curvature.
Inflation would have expanded the size of the observable universe so much that local curvature would be unnoticeable.
Rapid galaxy formation during inflation would have smoothed out local variations in density of material, and therefore in its curvature.