Further, I submit that any HFT will only place a buy/sell spread in the case where the volume is high enough that they can complete their purchases within seconds or at most minutes.
At best an HFT will cut a few minutes (more often seconds) off of the time of a trade. Anyone who is worried about waiting a few minutes for a trade to complete is Doing It Wrong. Therefore, the "liquidity" HFTs provide is only in the cases where it's not truly needed because the volume is high enough to provide it anyway.
I've traded in a lot of stocks where there was very little liquidity, and fewer than a few dozen trades would happen per day. I'd sometimes wait hours for a trade to complete. Where are all the HFTs providing me "liquidity"? They weren't anywhere to be found, because in the cases where the volume is too low HFTs can't make a sure bet. And when the volume is high, they aren't needed. So what good are they again? At any point that an HFT is willing to buy stock, it's because there's a high likelihood that someone will show up to pay more after a few seconds or minutes.
IMO the popular media actually has it right. HFTs really are just stealing pennies on every transaction, because they only enter a stock and "add liquidity" if and when the stock doesn't need it.
The onus isn't on me to prove they aren't providing liquidity, but on the HFTs to prove they are, and the OA doesn't even come close. In every example OP gives, the people actually buying and/or selling stock would have been better off without the HFTs in the mix (at best their trades were a few minutes faster).
If we just taxed or put a fee on a "short term hold" of a stock, say less than one day, then high frequency trading would vanish. I see HFTs as a parasite on a broken system, nothing more, and I'm shocked that so many HNers idolize them.