I understand that the traditional transition designs weren't perfectly round, but they were sufficiently so, that any plunger would work. My low-flow Kohler is so far from round, (the length of the opening is about four times the width) that no round plunger, however pliable, will work.
I'm quite surprised that there isn't a substantial outcry about this. I haven't been successful with a closet auger, and I even tried the "bellows" type on top of the seat to clear a blockage with no success.
I succeeded once with abruptly dashing about three gallons of water from a bucket into the toilet: and another time when that failed too, I waited over night with the bowl full and just before calling a plumber I tried one more time to flush, and it cleared.
It still seems to me that an elongated plunger would be a logical solution. Maybe most folks don't have clogs any more, or are happy to call a professional first thing...