You forget that for every buyer there is also a seller. If HFTs push the markets higher slightly faster because of new public info then while it might be bad f

You forget that for every buyer there is also a seller. If HFTs push the markets higher slightly faster because of new public info then while it might be bad for you if you are buying on that news, it's great for whoever already owns the stock and is the one selling to you. The same applies to your 3rd point. It might be a tax on whoever initiated the large trade, but it's a benefit to whoever is on the other side of the trade. HFTs put new information into the market much faster than humans ever could making them more efficient. They're also doing it at a lower cost than human market makers ever did.