Why aren't faculty applications peer-reviewed?
They are.  Applications for faculty positions are typically reviewed by a search committee, which is made up of academics.  This is a form of peer review.  

It is true that sometimes the applicant and search committee may be from the same institution when a job application is reviewed, while funding agencies and journals often do not permit that situation.  The reason is that it is not feasible to eliminate all potential conflicts of interest.  In other words, it is hard to obtain external reviewers for something like a search committee.  Also, the members of the search committee know more about their institution's needs than an external reviewer does.