As an Oxford grad I don't really see how employing Oxbridge students per se brings the reputation of the firm up. In fact, a fair number of fellow "jurisprudence" students are totally not fit for teamworking, the corporate environment, or working with others in general, because of their personality traits. Likewise, I believe that oftentimes better candidates can be found at RG and non-RG universities: the candidates that will be a better fit for the firm's long-term success. What Oxbridge students do get, however, is a massive advantage when it comes to applying. For instance, pre-covid firms would hold interviews in Oxford, so students did not have to travel to London and could prep at ease. Also, firms keep coming all the time and organise free drinks, dinners, and other events in Oxford, which provides students with massive netwoking opportunities, again, at ease. Moreover, the careers service is very OP, with ex magic circle recruiters going through your application with you. These advantage partly explain why it seems that Oxbridge students are so often recruited; they just have massive advantages over other applicants.