Stocks trade when there is a buyer and a seller. An exchange you are not officially listed on is unlikely to have many sellers and so they may not have any stock when you want to buy. Of course they can keep a lot of stock on hand (that is become a market maker), but that means they arbitrage games (either they or someone else), and if their volume of trades is too low (which it will be because few traders think to to use them) they are going to lose money on that deal.

Back in 1800 an exchange was a place where a lot of buyers and sellers agreed to meet up so that you had good odds of finding a buyer when you wanted to sell. The exchange happened by exchanging papers which then got sent to the company to know how the new owners were.

This gets at why there were a lot more exchanges in the past than now. Ownership is recorded electronically (you can get paper but almost nobody does) do you don't need to send papers into head quarters. We also have fast communication so can have your agent take care of things in New York in seconds no matter where in the world you are - in 1800 you had to physically go to an exchange (or send an agent).

An unlisted exchange is similar to a dark pool. The company whoes stock is traded on one will treat the trade like any other dark pool. However if they are trying to operate like a listed exchange they will doing other exchange like things (posting prices), so you get the worst of both worlds.