I'm being called oblivious by people who confuse HFT and market making which each other. That's cute.
There are companies that provide liquidity. They do nothing else. They don't take a position in the market. Its their job to quote both a bid and an ask and to trade with anyone who wants to hit those quotes. They are not allowed to not quote a price, unless trading is suspended. Those are called market-makers. They need to be able to change their quotes quickly, because being taken out on one side of the market creates positional risk for them. The only time they make money is when they can trigger a buy and a sell at the same time. If they cant do that, they have to hedge their position. They have to compete on spread with other market makers, which is possible to do in 2 ways - being fastest to quote or having a narrower spread. Trades at the price are executed in the order of submission.
There are companies that engage in statistical arbitrage. They look for opportunities that are statistical in nature. Think of technical analysis but in a way that works. Think stock A and stock B being more correlated than price reflects. They want to execute fast because those opportunities do not exist for long. This kind of trading smoothens out the curve and smooth curves are nice to have, mathematically speaking.
There are HFT firms who scalp dodginess in price by renting colocated servers. Very tiny but almost guaranteed returns if they can get execution. Nothing wrong with that either. Low margin business model.
Then there are companies, or rather teams inside companies, that send buy and sell orders into the exchange that they never want to execute, on millisecond timescales, to disrupt the market. They are trying, in simplified terms, to create signals for other market participants that do not really exist, and then execute trades that they know will be profitable by exploiting other participants for whom they generated buy signals. This is your evil HFT. The T in HFT is a misnomer, because they dont really trade. They abuse stock exchange mechanics to fuck with other market participants and then try to rob them. This is mostly illegal and not allowed by the exchanges themselves. The problem here is to prove that someone didnt play by the rules. Google "optiver the hammer" for an example of a couple years ago. They have counter-intelligence teams whose entire job is to not trade the market for profit but to ruin other companies profits to drive them out of business. But most of this is illegal, its just difficult to prosecute.
The problem with banning folks is that most trading companies engage in all of these things at the same time. There are market making teams at optiver and there are evil HFT teams at optiver and if you ban optiver, you wipe out a major market maker which leaves the stock exchange exposed.
Another problem with "banning HFT" is that where do you draw the line? Market participants can suddenly not try to get their trades executed anymore? Maybe that's beneficial to the market as a whole, but how do you even execute such a rule?