Different exchanges have different requirements to have a stock listed with them. It's a private business, no one who is smart wants a single nationalized stock exchange.
Stock Exchange is the private company that belongs to investors. There are two major Exchanges NYSE and NASDAQ. NYSE took over the AMEX Exchange.
NASDAQ was trying to take over the NYSE but monopoly comity did not approve it. If there would be one exchange that this exchange would keep the monopoly and all investors would have to pay big money to this exchange to be able to invest. All the investment company would have pay several times bigger than now Exchange fees and so on.
I hope it answers on your question
Yes, one could work, even one global exchange. But national or global, it then would be a monopoly.
The exchanges in the U.S. are not owned by the government. They are all publicly traded corporations.
There are so many mergers and acquisitions occurring that you may eventually get your wish.
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Additional:
A company is only listed in one exchange, but identical commodities and futures are traded in many different exchanges.
There are some companies that specialize in carefully watching for differences in price. Within microseconds of a difference appearing, they will make a buy in one exchange and a sale in another to capture the price of the disparity.
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Stock exchange is a market place where sellers and buyers of investments(shares and bonds) can complete the transaction of buying and selling through middlemen(brokers)
It is just like a vegetable market where sellers and buyers of vegetables transact through middle men.
These vegetable markets are street markets,colony markets,town markets,local markets,state,national and international markets.These serve the different needs of concerned local customers as for their convenience.
Stock exchanges (share market) at different places like national and international markets serve the different needs of buyers and sellers of shares. So many markets are required at different places.
The speciality of stock exchange is buyers and sellers need not meet personally to take delivery and make payment. Transactions can be completed through brokers.
There used to be lots of provincial stock exchanges (like Liverpool, UK).
Why can only one national stock exchange do all the working?