For 50 years the "mean-field" method based on the celebrated Bogoliubov- de Gennes equations has been routinely used to analyse problems in the theory of inhomogeneous Fermi superfluids.When the pairing state is s-wave and the condensate is at rest,as in most applications to classic superconductors,there seems no reason to suspect that this method is not reliable.However,it has also been used over the last 15 years to discuss more complicated situations;in particular,it forms the basis for claims that so-called p+ip Fermi superfluids such as strontium ruthenate can be used to implement topological quantum computing (TQC).In this talk I analyze the basis of the method and adduce reasons to doubt that for applications such as TQC,where one is interested not in macroscopic averages as in most traditional condensed-matter applications but in the delicate properties of individual quantum states,the method is even qualitatively reliable.