I think LOR's can speak volumes about the quality (or should I say apparent quality) of an applicant -- depending on who writes it, and what and how it's written. Even more important is who READS it.
Having recently flown a trip with a check airman that is FREQUENTLY on the interview panel, LOR's and verbal recommendations can carry a lot of weight. While we finished breakfast one day, he actually got someone scheduled for an interview based on a Company pilot's recommendation directed to this check airman.
Why is this? I think Reepicheep hit the nail on the head when he/she said that it's a form of screening. With so many qualified pilots looking for work, many companies are taking more efforts to hire based on personality, as well as their qualifications.
Again, this is only my opinion based on my experiences.