Mean reason to increase any node impedance is
related basically to increase the small signal gain.
Notice that the small signal gain is
gm.Ro (transconductance times resistance (or impedance))
Now, in the question, you are asking we have multi stage cascaded amplifier, why the impedance is chosen higher towards the end of the chain.
This statement is not always true, consider for
example three stage miller opamp (first and second stages are gain stages and they have similar small signal gains, and the last stage is buffer).
I am not sure but for exotic amplifiers such as nested miller compensation kind of amplifiers also this should be the case.
Now, the only place where this make sence is actually RF amplifier, now for that kind of aplication
signal to noise ratio at the output is important.
And it can be shown that in a multi stage amplifier next stages' noise is divided by the voltage gain square of the previous stage while reflecting equivalent gain to the input. So in short only input stage noise is important. Now, to reduce the input stage noise you have to burn more current (to increase input transconductance hence reduce equivalent input refered noise. If you burn more current, your impedance will be smaller (because
output resistance is proportional with 1/lambda/Id
if this is IC design or because of the bias point issue
you have to choose small resistor value if it is discrete). Now after the first amplification, you can scale the current without any noise penalty and increase small signal gain.