One of the key reason is to limit volatility. Indeed, it is sometimes better to have some pauses to calm down any aggressive movements.
That is why most firms hold their earning calls post or pre-market and not during opening hours. It allows analysts to fully integrate the information published by the firm before reacting.
Also, an exchange opened 24/7 would mainly benefit large institutions such as big banks, and probably hurt smaller stockholders, who cannot stay awake at any time to react appropriately to market movement. One could thus argue that the system is fairer as is. Chinese stock markets, which heavily rely on small holders (for the best and the worst) even have a pause at mid day.
However, a lot of firms use ADR and GDR (depositary receipts) in order to be quoted on several stock exchange. Therefore, they might de facto be quoted all around the clock. FX markets and derivatives (in particular OTC) also have larger opening hours than regular stocks. And to add a final element, some stock exchange such as NASDAQ organise a pre-market quotation, which helps determine the opening quote by surveying market participants, though no transactions are involved.