What polishing actually does
A "polish" is the abrasive removal of a thin layer of case metal to remove scratches and restore shine. Each polish takes off roughly 0.05 to 0.15 mm of material, depending on aggression. The first polish leaves the case still close to its original geometry. The third or fourth polish has noticeably rounded what were originally sharp lug bevels and chamfers; the case has lost the crisp facet lines that the case-maker designed in. Polishing is permanent; you cannot un-polish a case, you can only remake one (a CHF 3,000+ job done by a specialist).
Why vintage collectors object
Three reasons. First, geometry: a 1968 Rolex Submariner 5513 has a specific case shape with sharp bevels and faceted lugs. Three polishes later, the bevels are soft, the lugs look wider and shorter, the case is "potato"-shaped, and the watch is no longer faithful to what left the factory. Second, provenance: an unpolished vintage case is increasingly rare; collectors pay premiums of 20-40% for an unpolished example because they are time capsules. Third, patina: patina on a brushed steel surface (slight oxidation, microscopic warmth from wear) is part of the watch's history. Polishing erases it.
When polishing is fine
Modern watches with thick cases, especially heavily-used sport watches: a Submariner from 2010 onwards has plenty of meat for one or two careful polishes over its lifetime. Daily-driver pieces with no collector value: an entry-level Tudor, a Hamilton, a Seiko. Watches with truly destructive scratches (deep gouges from a fall or impact) where leaving them looks worse than gentle metalwork. Watches you have no intention of selling for 30 years: by the time the case wears thin, you will have made peace with the geometry shift, and the daily wear will mask it.
Brushed vs polished surfaces
A complication: most modern sport watches have a mix of brushed and polished surfaces on the case (Submariner: brushed lug tops, polished lug sides). A "polish" at the brand will refresh both, re-brushing where it should be brushed and re-polishing where it should be polished. A bad watchmaker will polish everything to a mirror finish, including surfaces that should be brushed; this looks terrible and immediately telegraphs "polished by an amateur". If you do polish, ensure your watchmaker confirms which surfaces are brushed vs polished on the original.
How to refresh without polishing
Three non-destructive options. Hand cleaning: warm water, soft toothbrush, gentle dish soap on the case (never on the dial), dry with a microfiber cloth. Removes most surface grime and finger oil without abrasion. Cape cod cloth or microfiber polish: removes shallow surface scratches by burnishing rather than abrading; recovers some shine without removing material. Bracelet only: a bracelet is much cheaper to replace than a case; if the bracelet is the worst-looking part, swap or polish only the bracelet and leave the case alone. Brand restoration: some brands (Patek, Lange) offer a "case restoration" that re-cuts bevels rather than just polishing; expensive but properly redoes geometry.
Buying advice
When buying vintage, look at the lug bevels. Sharp bevels = unpolished or lightly polished. Rounded, soft bevels = polished multiple times. Crisp 90-degree edges where the lug meets the case top = unpolished. Soft transitions, missing chamfers, lugs that look "fatter than the catalogue photo" = polished hard. An unpolished case from 1965 on a Rolex Sub or Speedmaster carries serious premium. When selling vintage, do not polish before listing; a polish to make a watch "look better in photos" usually destroys 15-25% of the value. See should I buy vintage? and patina vs damage.