The way I see it, most, if not all, of well defined problems amount to search (maze, chess, proving Fermat's last theorem). You search carefully for a long time, and at some moment you are done. With a poorly-defined problem, you never know if you're done: you need to operationalise it in a way that "makes sense" to you and other people and then possibly reoperationalise it again based on new data or intermediate results. This kind of activity demands flexibility; search is more about rigour and exhaustivity.