IIRC, the reasoning behind the need for buffering here is that, because the current level that must be passed by the current source depends on what load the opamp is driving, we obviously want to keep that load to a minimum.
To keep the op-amp in class A, the CCS has to be passing more current all the time than the load would take on its own. You can imagine what would happen if the load is demanding some of that current. As TK says, the opamp's output pair comes out of class A into a crippled push-pull.
Imagine also that you are driving a low-impedance load using a CCS set-up like this. You have to bias the opamp with a buttload of current to keep it in class A. Then you run the risk of a couple of things: tempature problems and current-limiting problems.
For example, let's say that our opamp is only capable of delivering 40mA maximum. By putting something like a 22mA current source on the output of the opamp, you will likely make the chip perform worse than with no biasing at all. At this level, you'll most likely activate the current limiting circuitry of the opamp, plus you're raising the operating temperature of the chip significantly.
So, buffering it is! :grin: