Batch orders are seemingly a good idea. Several markets operate in an auction style batches, where each participant presents their schedule (a list of possible prices coupled with an amount to buy or sell for each price) and at set intervals a computer determines the price and quantity that clear the market. We have algorithms that do this in a utility-maximising way, but it is definitely more effort on the part of the traders. Electricity exchanges are the only ones I can think that use this method. APX, for example, does this for day-ahead UK power trading.
But you don't actually need auctions for this to work. You can use a similar public-outcry method (just like in the NYSE) but separated by breaks. The London Metal Exchange does this in its trading sessions. They are split up into 5 minute intervals, each of which can only be used to trade one particular metal. It's pretty cool to watch.
Both these markets are very liquid, so I doubt splitting up the trading day of even the busyest exchanges (NYSE, NASDAQ, LSE) would cause any perceivable damage to the market's fluidity.
One way to make your old car run better is to look up the price of a new model.