Currency markets grew up on their own, unregulated. The fiat money traded doesn't have a claim on any real assets. In principal, securities markets are regulated and the securities represent a claim on dividends, interest and corporate assets.
Just because we have the technology and the interest to trade 24 hours a day, should we? I think it is a good goal to improve market access and efficiency, but 24/7 trading may not achieve this. It is probably worth trying, but I think that currently, most of the volume in equity markets occurs at the open and the close of trading.
I can make the case that moving in the other direction will achieve the goals of equal access and efficiency, too. Make the capital markets a dutch auction (accept all orders and set one market clearing price for each security) and have one, two, or three global sessions a day.
I like trading equities, but my gut tells me that 24/7 trading will increase regulatory, settlement and spread costs in exchange for some convenience.
Chris