No. all stocks are able to trade on all exchanges and dark pools. The main rule governing stock trading is that every trade has to take place between the best bid displayed at any exchange and the best offer at any exchange. This means that no exchange is allowed to execute a trade that is not at least the best price in the market.

Furthermore, you wouldn't want your stock to just trade at this exchange. Hypothetically if you only wanted your stock to trade on IEX you would probably be missing out offers to buy and sell that are better than what's displayed there.

Picture this. In the below example we have three exchanges NYSE (New York Stock Exchange), NASD(Nasdaq) and IEX ("Investors" Exchange). They all have liquidity displayed at different levels. According to the rule above no trade can occur outside 11.99-12.01 because the best offer to buy is 11.99 at NASD and the best offer to sell is 12.01 at NYSE. IEX can't execute any displayed orders.

Prices| NYSE| NASD| IEX

12.03| S 300| S200| S100

12.02| S 200| S100| _____

12.01| S 100|______ |_____

12.00| ______|______ |_____

11.99| ______| B100|_____

11.98| B100| B200 | S100

11.97| B200| B300 | S200

[email protected] [email protected] NYSE

Exchange competition itself keeps exchange fees low so that no one exchange holds all the liquidity and can then raise their fees per trade. The Futures market has a lot less competition where CME (Chicago Mercantile Exchange) dominates the market.