A slightly different motivation for fourier integral operators and pseudo-differential operators is given in the first chapter of book. In first chapter of this book, V.Guillemin presents this subject from the conormal bundles point of view and then shows how pseudo-differential operators are a special case of operators coming out of the Fourier distributions.
Section 3 of this chapter also provides a historic outline of this theory.
Interesting, Guillemin also shows here that pseudo-differential operators can be used to fine tune the theory of conormal distributions themselves -- giving a natural but unexpected application of pseudo-differential operators.