What are you hiring for?
If you're trying to hire someone who presents well to strangers, creates documents without typos, is good at seeking out interesting new opportunities, can think on her feet in an interview and can network with strangers in search of a goal, your current hiring system is probably perfect.
Unfortunately, those skills don't apply to most jobs.
As a result, we end up hiring people who are good at self-marketing, not at what we need them to do.
It may very well be that this programmer or that cleaning person or this animator is absolutely terrible at the things that make it easy to get hired. Is there anything wrong with that? Isn't the entire point of a hiring process to separate the people who will be good at the job from those that won't? Why is "clever cover-letter writing" or "willingness to travel across town on spec for an interview" a leading indicator of that?