Thinking about the standard flipper position, the only shots that are possible are the ones in the fan layout. It's impossible to have anything but shots that go in a straight line from the flippers to some target, unless you are willing to count flop shots that only go halfway up the play field and then arc around. Due to the position of the flippers, all the shots have to radiate out from the bottom center of the playfield.
I guess that's the motivation for having a third or fourth flipper halfway up the playfield on some machines, so things get more varied.
I seem to remember machines that tried to break that pattern and had creative shots that do not follow the fan, but I can't recall any of them outright now (that's going back to the seventies and early eighties). All I can remember is that there were some machines that had "impossible" shots that could happen only by accident, from weird rebounds and the like, and how angry I was at the stupid machine that asked me to do impossible things. But, maybe, that might just be because that was more than forty years ago and my skill level wasn't all that high.
It would be interesting though to compile a list of machines with "impossible" shots. Anyone have any suggestions? Are there any "utter design fails" in pinball history?