> I don't exactly get how HFT also makes it low cost
Because most HFT firms are also market makers. You can see them basically as middlemen that are mandated by the exchange to provide liquidity on both bid and ask by the market. These liquidity mandates reduce the spread for other traders, and in exchange market makers have lower, or even positive fees (i.e. they are _paid_ to trade).
Usually, market makers use these rebates to earn money by taking a passive order risk on behalf of an aggressive order from a flow they bought.
Think of it that way:
You're an exchange, you want people to trade on your platform, that's how you earn money.
For people to trade on your platform, you need liquidity, actual shares to buy and sell. So you invite market makers on your platform, and sign a contract with them, along the lines of "you have 0 trading fee but in exchange you need to provide $X of liquidity on bid and ask at any time and ensure a spread <Ybps".
Market makers accepting to on-board now have to somehow make a living while providing liquidity, but this is a risky business, because they are basically market making for people that are _more_ informed than them (they have adverse selection by design), and they have to respect their mandate of providing liquidity. That is, if a stock goes down, and people start selling it, the market maker still need to provide liquidity for sellers and buyers, which means maybe he will have to actually buy these shares that are tanking.
Usually the pure market making mandate is close to 0 profit, unless you spice it up with some other strategy. Taking passive order risk, netting order flow, maybe short term technical alpha, etc.
You can think of market makers and HFT basically as the same people. If you trade at high frequency, you're playing on micro changes in price, there's only so much a stock price can realistically move in 1s. HFT is only viable if you have very low, or no transaction cost. That's why there's a natural overlap between HFTs and MM.