Incentives for professors to write recommendation letters Is one incentive their ability to communicate their perceptiveness to people in their general community?

Are there other incentives?
The principal reason for writing any letter of recommendation is to benefit the person for whom you are writing it.  If a student is talented, helping him or her get into a good program is its own incentive.  I can't imagine writing a letter with the motive of showing off my perceptiveness.

An additional motive is that others wrote letters for the writer once, and he/she can show gratitude by paying it forward.  From David Keyes' excellent essay on procuring reference letters:


  Everyone in a position to write a career-changing letter of reference
  is there by the grace of earlier generations of mentors at school or
  work who poured their lives into today's writer and then wrote about
  the results in now dusty letters. The only gifts today's authors
  expect from today's candidates are those "in kind" or better to be
  delivered to tomorrow's candidates, in one-way cross-generational
  equity. Writers have their own rewards in the success of their
  protégés, and though they will moan to each other about the burden,
  they recognize that reference letters are key components of an
  imperfect system that nevertheless is on the whole effective in
  keeping their discipline healthy and growing.