Why shouldn't you use the emitter of a BJT NPN Transistor as a current source?
A current source should have high impedance.

Looking in to the emitter of a BJT in forward active mode you see a low impedance.

This means the base acts more like a constant voltage source (with a value of Vbase - 0.7 V) than like a constant current source.

This circuit is commonly used when a voltage source is wanted. It is called an emitter follower. The controlling signal is applied to the base, not the collector.

Another similar configuration is the common base amplfier. For common base, the controlling signal is applied to the emitter, and an output current is produced at the collector. This acts as a near-unity gain current buffer, much like the emitter follower is a unity-gain voltage buffer.