No let’s take an example with 2 pools with 100% pledge ( s’=σ’ to simplify things), and let’s take a0=5
One big pool which is saturated (s’=σ’=z0) :
s^2/z^2=1
so its reward formula : f= R/6*( σ’+5 * σ’) = R/6*( 6*σ’) =R * σ’
One small pool saturated at 1% (s’/z0=0.01):
s^2/z^2= (0.01)^2 = 0.00001
so its reward formula : f= R/6*( 1.00005 * σ’) ~= R/6 * σ’
One get a RoS 6 times higher than the other. If you call that fair, we don’t have the same notion of fairness! 