Quite simply, you can’t have “perfect round” because the geometric primitives that SketchUp manipulates are edges and faces. Inside SketchUp, under the hood, there are no arcs, and hence no circles.
You can approximate by increasing the number of segments, but at some combination of higher segment counts/smaller radii you come up against another limitation of SketchUp: How it determines if edges share an endpoint. Once the distance between end points become too small, SketchUp can’t determine if they are intended to be coincident - with unpredictable results. This can be overcome using the “Dave Method”:
Why? In almost all use cases, especially at smaller radii, a suitably segmented approximation of a circle is indistinguishable from a true circular arc.