It is just an incremental improvement. The damage is done and the anodization is gone on those spots, and no amount of polish is going to put it back. It's like paint that's been chipped off. All that a small amount of polish does here is clean up the dirt and oxidation, and make them less visible. In some case, and I suspect here, it can make it look a lot better, but it isn't going to look brand new ever again. This won't work on a large bare spot like the kind on crankarms caused by wear from the strap.

I haven't tried Mothers but assume it's similar to other metal polishes.

The OP asked for 30 second fixes. That's really the only one.

Removing the anodizing and going for full polish is about the only way to make them look 'new' again, but the look is completely different than the silky satin of anodized parts. I like the look of polished bare aluminum too, and was mostly pointing out that it is different. Where I live, polished parts take about 6 months to oxidize to milky nickel, but as [MENTION=403744]plonz[/MENTION] pointed out, it isn't that hard to buff them up again to a full shine once this happens. Before the mid 70s or so, the vast majority of bike parts were bare polished aluminum and had to be repolished periodically. Anodizing 'fixed' that problem.

If you wanted to go all in, they could be taken to a plater and re-anodized.