For the Hall-Héroult process, the solubility of alumina in flux seems to be important. But why should I care about the persence of alumina in the bath? I can use feeder to keep the concentration constant because electrolysis decomposes $\ce{Al2O3}$. It can be 0.1% or 10% what would be the difference? Concentrations does not affect decomposition voltages of the components, so the voltage would only decompose $\ce{Al2O3}$ and would not touch the flux.
I have found the answer! The limitation is in the current you can apply (limiting current) If you exceed it - the anode effect may occur and NaFAlF3 will start to decompose instead of alumina. So your cell will make you rich faster if the solubility is higher!