Output Impedance of BJT/Mosfet amplifiers
But these transistors are Transconductance amplifiers 'by birth'. I
  mean they give output current proportional to the input voltage.


When operated as a common source/emitter amplifier your point is true. When operated as common drain/collector, the output impedance is low. Typically, for a BJT using the emitter as an output (virtually unity gain), the transistor can feed a wide range of loads without much change in the output voltage.

The desired output is usually low impedance for such things as audio power amplifiers (push-pull common collector/drain) because they need to drive low impedances such as 8 ohm speakers.