Electrolytes in electrochemical half cells
For example, a silver electrode is immersed in a silver solution and so on, but is why is this necessary? Surely any positive metal ion will do?


There is a fundamental reason, which is the Nernst equation. It requires that the metal be in contact with its own ions. What is the functional meaning of the electrode potential? It is the tendency of an ion to reduce itself. Yes one can make salt water battery by dipping an iron nail (or copper) in one half cell and a piece of aluminum in another half cell but you cannot predict the cell potential beforehand.