The oxide protects the plate metal from corrosion, if
you need to protect both plates then you double the
dielectric thickness yet only use one of the two Al2O3
layers for its purpose (anode). So you then need twice
the plate area, meaning about sqrt(2) times the radius
or twice the height or some combination in between.
I have nonpolarized aluminum electrolytics in the parts
bins, but keep very few around. Nowadays most of my
work is low voltage where ceramics give a better board
density (no can, no plug, low height surface mount...).