Mentoring systems - Are they as effective as they could be?

Most reputed companies have an effective mentoring system in place, where new employees are assigned mentors, who will take their mentees’ career goals into account while helping them chart out their personal and professional paths. A mentor should be able to play the roles of ally, catalyst, networker, advocate, personal and professional developer, information source, listener, emotional supporter, role model and coach. The mentee should be a learner, self-developer, communicator, listener and implementer.

Would these mentoring systems be more effective if mentees had a say in whom they would like to have as their mentors, or is it better that they learn to look up to new types of people within their organisations rather than those they might have more in common with?