>E.g. no HFT firm should be able to make a profit from such a stock market. Selling stocks earlier and often should result in a penalty or percentage being taken away as a fee.
Maybe by "HFT" you only mean "those evil hedge funds that are pushing companies to chase next quarters' earnings", but there's nothing fundamentally wrong with high frequency trading. Market making[1] is high frequency trading, and basically involves offering to both buy and sell and given stock, and pocketing the spread. That increases liquidity, making it easier for other traders to buy/sell stock without taking a huge loss. It's unclear why you'd want to ban this, or how you'd distinguish this from whatever evil HFT you actually want to ban.