I've never bought the liquidity argument. Ordinary investors don't need to buy and sell at any time. They'd be happy buying and selling once a day (as with mutual funds).
What if the market consisted of a deep daily or hourly auction with lots of buyers and sellers matched up to discover a fair price? How is the current system better than that?
I'm currently launching an exchange. Liquidity is EVERYTHING. Your hourly auction idea is one way to provide it of course, and some exchanges do just this at special times, or at start of trading.
There really isn't a 'current' system actually, at least not as you probably understand it. There are hundreds of markets, with different rules, many of them can place orders between them.
None of this shows for someone putting in a 'buy' at E*Trade, though.
Prices become erratic and jump around more, so it's much hard to predict at what price you'll be able to sell. News events related to a stock tend to have an bigger impact on the price as it's riskier to hold on to stock when negative news comes out (and vice versa).
Your system might be more fair, but not one would use it. Traders want an exchange where they can buy/sell as soon as they receive new information, not in the future when everyone else has same information.
Settlement on share trades is not real time, and no one cares from a liquidity perspective. Settlement risk is a different question.
Who is convinced that these traders actually need to exist?
The share market's function in the broader world is to link long term investors with those who need long term capital for investment in the productive economy. Trading beyond monthly seems superfluous to me.
Today's markets don't operate 24/7 (they close at night for instance), and yet everyone uses them because they have no choice. Limiting HFT can happen through regulation.
What if the market consisted of a deep daily or hourly auction with lots of buyers and sellers matched up to discover a fair price? How is the current system better than that?