This is obviously not true, because HFT makes money, but you could say that HFT contributes to getting markets closer to being efficient.
Having efficient markets is worthwhile for society because an efficient, liquid market provides a more accurate picture of the "actual" value of things.
If you buy this argument, then HFT would be contributing to finding truth, which is inherently valuable in the eyes of many people.
At the end of the day, HFT is one of those things that people just get jelly about because someone makes money on something they dont understand and gets insanely rich "doing nothing".
What people get mad about is completely arbitrary. Everyone hates google because ads, but without google, their world would barely operate. Everyone hates facebook because fake news but nobody has the balls to actually not use facebook. A social network.
Everyone hates uber because "scandals" and poor drivers not being paid but still uses it because comfortable.
I'm not really in the stock market but when I want to sell stock, I'd rather there be some market maker who is obligated to buy it. Maybe he makes more money off of me than I ever will selling stock to him, but that one time when nobody else wants the falling stock and I potentially use a large chunk of my savings, I really need them.
Consumers sit on some amazingly high horses sometimes.
Also, there's a lot of straw man argumentation in your post. Consumers can and do make sacrifices of utility in line with their values, even if such behavior is a standard deviation or two outside the norm. And while your argument for market making is sound, do you really need to make that trade within milliseconds, or would you be equally happy as long as it closed within a couple of minutes? You seem oblivious to the possibility that your stock might be falling due to a liquidity event caused by a race condition, for example, although in cases such as the 'flash crash' such trades are usually unwound afterwards, presumably at considerable expense.
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?
Also, you really need to work on your manners, which is why I'm not going to bother addressing the rest of your remarks. Perhaps we can have a more constructive conversation some other time.
This is well-known. But for some reason, only kids trading in their parents basement, across the ocean, over a non-fibre connection to the internet, get charged and convicted.