Pull quotes do not belong on the web. They are out-of-place anachronisms from print publications, intended to entice a reader flipping through pages of a magazine, which does not translate to how people read on a browser. There should be stronger stigmatization of pull quotes in digital design than of using Papyrus and Comic Sans, on the same level as pop-up ads and auto-playing video.
Pull quotes _demand_ that the reader draw their eyes away from the article text just to re-read something they just read seconds ago, or are just about to read. These quotes scream with font size increased +10pt, and random words capitalized. They slow down reading, break concentration, and destroy the flow and pacing of the writer's craft.