Why doesn't LinkedIn have a "Mentorship" box in their "Opportunity Preferences" which lets professionals express that they're open to helping students/young professional with career advice/decisions. And if this was checked, a mentee would be able to InMail the potential mentor without needing a premium account. Prevent abuse by allowing mentor to mark a mentee request as spam, in which case the individual is blocked from participating in the mentorship program.
The opportunity here is that many kids lack professional role models so let's do a better job of matching them with advisors, even if it's just a virtual relationship.
LI could also decide to make mentorship one of the attributes they care about, and give people the option of adding this as an accomplishments field to their profile based on double opt-in disclosure of "Person X menteed Person Y."
Meg, Jeff - this would be a great LinkedIn For Good project, no?