Everyone loves polished aluminum, but you typically have to pay a good 30% more for it vs. any other finish. Since polishing is a simple process requiring widely-available tools, I thought I could probably get away with taking care of it myself on a some dull-finish or anodized rims. My concern is that I would remove enough material with the polishing wheel to affect the structural integrity of the rim walls, especially on newer rims that are built with very tight strength-weight tolerances.
If you're actually just polishing, you should remove very little material. I recently polished aluminium to a mirror finish in work (a very different setup as I had to keep the surface perfectly flat as well, but it's indicative). I removed only about 10 microns (but that's the limit of my Vernier calipers).
Braking abrades rims more than this, which is why rims usually have wear indicating grooves, which are considerably deeper. If you try to polish out deep scratches you might reduce the life of the rim, but look out for the wear indicators which should still show plenty of depth. If the bike is very old it might not have wear indicators. If you don't have wear lines, or you're polishing a face that's not used for braking, you should be careful to remove the absolute minimum material.
If you've got ultra-light rims not designed for rim braking, caution suggests you don't do anything to them. But the combination of aluminium, light weight, and disc brakes would be rare.
You also need to be absolutely certain to remove any polishing residue, and to make sure that you don't make the rim slippery. I'd start by doing the back wheel, and a section of the wheel on both sides, then clean it up and test ride it. You don't want to feel a difference in back braking as the wheel rotates, whatever the conditions. This will also indicate something else: The finish might not stay nice at long as you'd like. Brake pads grind the rims. Slowly but enough to unpolish the surface before long.
I would not try to polish off an anodized finish. It's hard and you would probably have a difficult time getting it off evenly.
For bare aluminum - go for it. Note that the AL may have a clearcoat finish on it already though.
Polishing will take off very little material - nowhere near enough to change the strength of a rim significantly (assuming you are starting with a fairly high grit - at least 800). I'd clearcoat the polished surface with polyurethane, making sure to keep it off the braking surface.