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First of all this topology is not a voltage amplifier, diode connection at the load causes dropping of the output impedance to 1/gm, hence gain will be around one -roughly-, but it still a current amplifier
for common mode feedback, you need it when you have two series current sources with error current (difference in their currents) between them so this error in currents will flow in the output impedance which is high impedance in case of voltage amplifier, hence it will lead to a high voltage error in this node, by super position the voltage of this node will equal to the voltage you have calculated (say Vdd/2) plus this error voltage (Ierror * Rout) which will result in that one of the transistors in your stack will go out of saturation (the output node voltage will go up or down near one of the rails)
for the attached image you only have one current source which is the tail current source, so you don't have the problem, but considering that the load is supposed to be current source that will be biased with a biasing voltage this will lead to the error in currents we have talked about, so you have to use CMFB
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