The need for a current source in an emitter follower
When biasing a transistor, you want to Q point to be stable. Since \$\beta\$ varies a lot, you want to design in such a way that changes in \$\beta\$ do not disturb the bias point. 

By placing a current source there, \$I_E\$ will not depend on \$\beta\$ (and \$I_C\approx I_E\$) and that way you can keep the transistor in the active region regardless of changes in \$\beta\$.