The NaOH reacts MUCH, MUCH more strongly to the aluminium-oxide anodizing. The initial reduction takes place quickly and the bare aluminium is taken off much slower. Besides, the rate-limiting step is how much base you have on the surface. Apply just a little, just sufficient to react with the anodizing, and that's all that's used in the reaction. In most cases, you have to re-apply more because the initial amount was insufficient. Very little is left to react with the aluminium and even then, that reaction is much, much slower anyway.
Follow up with some Mother's or BlueMagic metal-polish and you've got a nice shiny surface.
Those who shy away from this procedure have obviously not done it.