The following question asked recently on a forum is fairly typical and I'll try to answer it very briefly:
"I think any piece is better off in private hands if fairly insignificant, what would they do in museum warehouses, gather dust?"In most cases the artefacts not on display do metaphorically just gather dust but they are normally available on request and, in theory at least, they are preserved (much like evidence from a crime scene) in case further research in the future may shed fresh light. Methodology and technology are constantly improving and, for instance, a present-day re-examination of pottery sherds kept from an excavation in, say, the 1930s may result in entirely different conclusions from the original ones. What may seem "minor" or "insignificant" now might well prove to be extremely valuable to future generations.
Nor is the fact that many of the artefacts are apparently "identical" a reason to dispose of "surplus" examples. The notion of a "duplicate" is just 'baseball card mentality', entrenched in thinking of artefacts as mere art objects to fill gaps in collections. There is no such thing as a "duplicate" in the conduct of archaeological inquiry. In the world of academic research, the very fact that many of the artefacts are seemingly alike can be invaluable in studies such as cultural development investigation or quantitative analysis.
For a very basic example, let's take a "minor" and "insignificant" artefact found in huge quantities. A study of Firmalampen (a type of Roman lamp) a few years ago (Schneider 1993) shattered some earlier theories, set new standards in classifying the type, and enabled far more accurate appraisal of those found in excavations (and thus the site itself). The study was based on an examination of hundreds of superficially similar lamps (both complete and bare fragments) kept in the storage of museums throughout parts of Western Europe. Verified knowledge of their findspot played a vital role and, since chemical analysis was involved, mere photographs were not sufficient. Of course, such a study would not have been possible if the lamps had been dispersed to the market decades ago.
Police forces store evidence, paleontologists store fossils, mineralogists store meteorites, archaeologists store sherds, and so on. It would be rather simplistic to assume they all do so out of a childish resentment of non-professionals or an addiction for compulsive hoarding. Who knows what fresh insights into our past those dozens of identical pots currently gathering dust may reveal in a few years time? But one thing is certain: future generations will not thank us for squandering them away just to please a few people today.
There may be room for museums deaccessioning in some cases but we do need to understand some of the reasons why they may be reluctant to do so. And in the meantime, it's worth bearing in mind that there are literally millions of artefacts already on the market or in private collections.
*For the purpose of this post, the term "museum" refers to any public institution which includes the storage and preservation of archaeological material as part of its objective, and is thus distinct from those which function purely as a form of art gallery.