FontLab’s Font Auditor supposedly flags “inflections”. The manual says that “it is better to replace such curves with two curves.” The accompanying picture shows an ’s’ curve like this:

I wrote “supposedly flags” because I don’t really see them flagged by Font Audit, though that option is checked in the ’options’ window. (Extrema without points are flagged, but that it seems is another matter.)
Now it is convenient to use ’S’ curves since that is what you can do with a Bezier curve that you can’t do with a quadratic spline.
What harm is done by inflections? Is it a question of functioning of the font? Of aesthetics? What is the issue here, if any?