It would fail as fast as any utopia can fail.
A discontinuity like that is not beneficial. In fact, it can be downright disastrous.
From the sound of it, you want trades within each epoch to all occur at the same price. Thus, if the price of a stock is $1, and I buy 10 shares (presumably finding a seller), it doesn't change the stock price, it merely decreases the number of shares for sale on the market at that time. You've engaged in price fixing. As a result, you could easily reach a situation where there are simply no sellers or no buyers because the fixed price is too far from the actual value people attribute to the stock.
Then, at the end of the epoch, all trades go through and we need to set a new price. But what do we set it to? If there were more sellers than buyers, we should clearly reduce the price. But do we reduce it to \$.99? \$90? \$0.50? \$0.01? We don't really have any useful information to set the price.
Alternatively, we permit people to decide what price they are willing to buy/sell the shares, and then they all get to act at the end of the epoch. If there was a buyer/seller match, then the sale goes through. Otherwise, after 6 hours, the market announces to you that you didn't actually buy/sell your stock. But how do you pair them up? Algorithms will be subject to abuse, and lots of simple algortihms simply don't work. You can't use any of the simple first-come-first-serve matching algorithms because that will instantly turn your market into an unofficial continuous shadow market with an official sweep every 6 hours.
In the end, you'd need the special kind of utopia where nobody questions why things are done the way they're done. Otherwise, you'll eventually have someone realize that the system has been made inefficient, and they'll invent a more efficient one.