Archaeologists do not get to keep what they find. Archaeologists don't get to keep the stuff they find because it doen't belong to them. In the United States, artifacts belong to the owner of the land where the artifacts were found, and the owner may donate them to a local museum or history center. If the artifacts are discovered on public lands, then they belong to the city, state, or federal government. There are also some strict laws to remind archaeologists that they cannot excavate site to acquire artifacts for their own personal enjoyment or profit.
Most artifacts end up in museums and univeristies where they can be studied and enjoyed by everyone.