Fame
While there aren't many (any) famous phlebotomists, there are plenty of famous people who have had their blood sucked, both for health reasons and for charity.
Working the local Red Cross Blood drive could lead to your chance brush with fame, if Jennifer Lawrence or Sam Smith stop by to donate some of their precious plasma. You never know what kind of celebrities will be facing your needle. Even the President of the United States and Royals need to get blood taken from time to time. Just think, you could be Phlebotomist to the Stars.