An exchange makes money by charging a percentage fee for each trade.
The only reason to be able to transfer stock shares from one exchange to another is to take advantage of arbitrage, that is differences in price between one exchange and another.
The price of a stock or even of bitcoin on one exchange varies from the price on another for a variety of reason including differences in volume between exchanges, the cost of getting FIAT into that exchange and the cost of getting FIAT out of that exchange.
If an exchange charges or passes along a fee to transfer USD, for instance, the price of bitcoin on that exchange will be higher.
It really does not serve the interests of a bitcoin exchange to have free transfers of stock shares out of that exchange.
It involves more work in programming, a greater need for security, and greater risk to them.
It would only make sense if a fee was charged, by the exchange for such transfers.
If something like that were implemented, it should, theoretically, lead to less price difference for a stock which is traded on several exchanges, between the price on those various exchanges. The problem is that eventually, there would be a flow of those shares from the exchange with less volume to the exchange with greater volume, and the smaller exchange would lose out.
It might deal with that problem by offering lower transaction and exchange fees. That would cut into the profits of the smaller exchange. People might buy the stock on the small exchange and sell on the larger exchange. But that would result in less supply on the smaller exchange, which would to higher prices on the small exchange, which might lead to people selling on that exchange. But, having such a flow through without a fee would lead to the death of the smaller exchange.
I've been working on a concept for an inter-exchange share transfer system. It would allow people to remove their shares from exchanges entirely (a la AsicMiner direct shares) then replace them on the exchange of their choice. Or just do a direct transfer. It would provide a valuable service as well as close the price gap between exchanges.
I'm not a coder, though I know some basics and understand limitations. If anyone is interested in this get in touch. I have it fairly well fleshed-out, and I have some ideas for how to make it profitable.