Why are aircraft painted at all?
Because of the flying billboard function. Marketing determines the colour scheme, not techical reasons such as weight savings (which is true) or drag reduction from paint (which is false).
Because of protection. The paint protects against small scratches from sand etc which may start fatigue cracks. If the polished skin is re-buffed 3 times a year it is closely scrutinised - but preventing is better than curing. Polishing removes a very thin layer of aluminium oxide and I could find no references that the amount of removed material would be a problem during the lifetime of an aircraft.
On a 737-800, the coat of paint weighs about 70 kg, on a B-777 about 200 kg. The cost increase due to higher maintenance requirement is about 60 kUSD in 1998 dollars or 85,000 dollars/year now, for an airline with 100 B737s this equates to higher maintenance cost of 8.5 mUSD/year. This is offset by the reduced fuel costs from the weight savings, depending on air miles.
Corrosion prevention is an often quoted reason for the coat of paint. However there is a specific type of corrosion occurring only on painted aircraft.
From a Boeing document:
Polished surfaces are protected from corrosion by regular buffing
after washing. Painting protects against oxidation, salts, and jet
fuel spills. However, unrepaired chips and cracks in paint collect
dirt and moisture and so may become corrosion sites. Painted surfaces
are also susceptible to filiform corrosion, or worm corrosion, which
begins between metallic surfaces and paint and erodes both. It creates
hydrogen and lifts up the paint layer as it travels across the
Another Boeing document addresses claims that paint may reduce drag. It effectively refutes these claims, stating that both painted and polished aeroplanes are aerodynamically clean. It does recommend to keep them that way, by washing all planes at least three times a year, due to accumulated dirt and insects which do cause increase of drag. Something that was found by the regular buffing of polished aircraft, I believe that in the past polished aircraft were found to have lower operating cost which was first attributed to weight savings but later turned out to be due to less insect residue.
All in all, aircraft are painted for good reason. And sometimes they are not painted, also for good reason.