Wait, you're saying that you know how to provide the same service BATS offers, at a lower price? Why are you whining about how evil they are when you could be making money competing with them?
Exchanges provide anonymity. How volatile would the market be if every time Soros or Buffet made a trade, a horde of followers-on tried to do the same thing.
They eliminate counterparty risk. If you sell some shares in exchange for $$, you get $$, period, even if the other party is broke.
They are centralized points at which the market can be regulated. How else can you discover insider trading?
They provide a market for every listed stock, whereas many thinly traded concerns would be essentially unpriceable for much of the day. Imagine what this would do to attempts to calculate risk, etc.
Market making can be and in fact already is done algorithmically, even on the NYSE. That issue is orthogonal to whether a security trades on an exchange or not.
Look to the FX or bond markets to see what happens without good, popular exchanges. These places are widely known to be rife with fraud, counterparty risk, and arbitrariness.
