I do not know the exact claim of the benefit of alum battery, but I think one of them is less corrosion.
Few days ago I boil a mix of water and ammonium alum. The alum water end up corroding the metal cup badly:
I believe that alum battery can be a big scam.
But, maybe the battery corrode different way. Boiling acid water will dissolve the metal, but we see battery terminal corrosion. It seems acid battery make the part not submerged in acid to corrode. Alum battery would make the part submerged in alkaline to corrode.
I think alum battery will produce much worse corrosion on battery.