Your second and third paragraphs are incorrect.
Day traders flipping stocks every few seconds won't lose money because of HFT firms, they'll lose money because of trading fees. Trading every few seconds is a wildly unrealistic strategy for most people to pursue on their own. On an average, per-trade basis the fees associated with buying and selling are several orders of magnitude higher than the profit margins of any HFT strategy. The only way your fees will even come close to the profit margins of an HFT are if your volume is such that you've become a market maker yourself. This is a very basic and fundamental tension that precludes HFT from being a competitive force to other traders engaging in speculation and investing.
Your final paragraph strikes me as ideologically bent, particularly with your use of the word "leech." It's an uncontroversial fact that HFT firms facilitate market making. HFT firms do sit on shares and offer them for sale. Most often they do this quickly, but occasionally they have holding times with longer horizons. What's more important than the turnaround time is the low latency with which they execute orders. Definitionally, HFT is engaging in market making because when someone wants to purchase a share, an HFT is ready to sell it to them. Likewise when someone wants to sell a share, an HFT is ready to buy it from them. This is quite literally, "making a market."
In point of fact, your hypothetical day trader would not be capable of buying shares every few seconds if it weren't for HFT (inadvisable though it may be). How do you propose they'd achieve the same kind of liquidity otherwise? By calling a broker? There are far fewer market makers than there are active investors. Passive investing activity with index funds also dwarfs the scale of HFTs. The straightforward conclusion that follows is that fewer, faster parties must exist to make markets for the many, comparatively slower investors.
This is an extremely well-studied subject; when you peel back the pomp and PR about HFT as an industry, you'll encounter an incontrovertible reality. There is no way to service modern trading activity happening every second without the HFT activity that happens every microsecond. By calling that latter activity "leeching", you read more like someone delivering an opinion rather than a cogent, well-informed and substantive criticism.