With 2.2 mA the transistor as emitter follower has an output impedance of some 12 Ohms.
That's not what is happening...
The emitter follower is the external part of a closed loop amplifier - it is just only a uni-polar output stage. No need to sink current...
Running the sim in LTSpice gives an output impedance of only 1mOhm.
Some significant advantages come with using an emitter follower:
-The current through the shunt reference remains basically constant - the classic circuit shares the bias current with the load.
-The bias resistor won't need to provide the load current - it can be larger.
-A wide range of load currents are challenging for a shunt circuit - in paticular if larger load currents than the max bias current are required.
-The power dissipation within the reference IC remains constant with changing load currents.
Cheers
Andreas