The use of changing wall angle to increase uniformity of a constant directivity horn is a different matter, because it addresses the loss of pattern control. What CuppaJoe is talking about is widening a very small area near the throat. This will not widen or narrow the pattern at any frequency. It might cause a reflection at high frequency, hopefully, out of band. But the pattern would not be set by this feature because the rest of the wall angle constricts radiation to a narrower pattern.