Earlier quoted context omitted.
Why should trading at that frequency be illegal? What is the optimal amount of trades per second one should be making? Once per second? Once per minute? Once per year? Even if there were such a number how could any bureaucrat ever arrive at the optimal frequency any particular market participant should be trading at?
Does the intrinsic value of a company change 29 000 times per second ? is this signal or noise ? Trading once per day and randomizing the order of trades would work nicely I think. There was a recent very good example of this concerning Apple : When Steve Jobs died, they kept the information secret and agreed with the stock exchange to suspend trading for a day. The time for everyone to think about what it meant for…
One of the primary benefits that market makers (which are often HFT firms) provide is the efficient transfer of risk. That is to say, the value of the company may not change thousands of times a second, but the willingness of existing holders of that stock to continue to do so may change rapidly. Or similarly some participant may suddenly need a hedge and buy this stock because it has the correlation their looking for. This is all to say that there are valid reasons for buying and selling a stock that have no direct (but some indirect) relationship with the value of that company. This is not a game played by retail investors, but it's not just played by HFT firms either. Institutional investors (e.g., my 401k money) will also use financial products in this way.
Or put a completely different way, I may sell my Apple shares because I need the cash back to help pay for a downpayment on my house. Did I sell those shares because I think the value of the company has suddenly changed? No. There are a myriad of reasons participants may move in and out of a position.