You're assuming the conclusion, that continuous buying and selling is the only possible way to run a market. But another way to run it would be to have an auction every five minutes. That way there are more buyers and sellers to match up, so it's more likely that everyone gets a fair price. And don't talk to me about liquidity - nobody really needs to trade that quickly.
In a way we have what you're suggesting. Look at what happens overnight when exchanges are closed. You see a big jump from the closing price to the opening price the next day. Even though you can't trade over that period the price still changes - you just restrict trading and price discovery to people who can do OTC or pre-market trading.
It's not as if people haven't tried other models, EBS who run one of the major currency exchanges restrict price updates to once every 100ms. They're losing customers to other exchanges who allow people to trade faster.
People with deep backgrounds in algorithmic game theory have been studying exchanges and auction design for a long time now. If someone could figure out a better design for exchanges, they'd be building it.
