Why are recommendation letters highly relied upon?
In a typical example, if someone has three socially close friends (including current colleagues, coworkers, past professors), then, his applications are always supported by strong recommendation letters.


No, that's not what "strong recommendation letter" means.

First, strong recommendation letters do not simply state the author's high personal regard for the student, but provide specific, personal, and credible detail supporting the applicant's potential for excellence.  I don't just want to know that someone thinks you'll succeed—I assume they wouldn't write you a letter if they thought otherwise.  I want to know why.  I want compelling evidence, not mere opinion.

Second, recommendation letters have more weight if they come from credible sources.  At a minimum, the author should work at a credible academic institution.  The best letter writers are themselves experienced, visible, active researchers, with documented experience mentoring and/or selecting candidates for admission/hiring/promotion at departments similar to the candidate's target.  For faculty promotion in my department, letters are essentially required to be from full professors, preferably in named/endowed positions, in top-10 computer science departments, and there is a strong preference for ACM/IEEE Fellows, NAE or NAS members, and major award winners (Turing, Gödel, Dijkstra, Gordon Bell, etc.).

The intersection of these two aspects of strong letters is direct comparisons with the applicant's peers.  An ideal PhD recommendation letter for my department includes sentences like "Among the 13 undergraduates I have mentored who went on to top-10 PhD programs in computer science, I would rank [applicant] roughly 3rd, well below [famous person who proved P=NP], but on par with [successful person] at MIT, [successful person] at Stanford, and [successful person] at CMU."