Heh. Yeah I remember that, it was wild.

I don't think most people are aware of the physical reality of what HFTs are doing.

Relevant quote from your wikipedia:

In May 2014, a CFTC report concluded that high-frequency traders "did not cause the Flash Crash, but contributed to it by demanding immediacy ahead of other market participants

Or as the article I linked puts it:

What turns out is happening is he's sitting physically in lower Manhattan when he makes his trades. When he pushes the "buy" button, the signal from his computer travels up the fiber optics along the west-side highway of Manhattan and through the Lincoln Tunnel. On the other side of the Lincoln Tunnel is one of the 13 stock exchanges, called the BATS Exchange founded by high-frequency traders.

They're sitting there, and they get the signal that he wants to buy first. ... They can see what he wants to do. They discern his desire to buy Microsoft, and they have faster connections to the 12 other exchanges that are scattered across New Jersey, and they race him to the other exchanges, buy all the Microsoft in front of him, and sell it back to him at a higher price.

HFT algorithms jumping on stubs seems pretty plausible to me. The whole thing is way too black box at this point, it's ridiculous that there isn't a clear answer.

Is there any reason not to regulate HFT out of existence ?

I understand that the stock market can be beneficial but High Frequency Trading?

It's just a parasite to the economy, sucking money without any benefit.