If they do maintain them, they reap a number of benefits including discounted pricing from trading platforms and IIRC, the ability to do naked short selling (which IMO should be off-limits for all trading firms). I'm not defending HFT here, just stating a fact that market makers are a part of the trading ecosystem.
Keep in mind that "making" and "taking" liquidity is not the same thing as buying and selling. Market makers are required to post both bids and offers. The difference is that market makers put their orders (buy or sell) on the "book", which means they are offering liquidity in both directions. The order that comes in to match (think "market" order to buy or sell) is the "taker". Firms that supply liquidity are rewarded by trading platforms (unsurprisingly, since those firms "make" their market), and firms that match those orders (takers), are charged for the service.
Not all HFT outfits are "market makers", but many are. I can't say specifically if Virtu is a market maker, even if I remembered :) The point is that liquidity providers don't pay for their trades, they are paid for them, so it's a natural fit for a smart HFT operation.
Out of curiosity -- why?
https://en.wikipedia.org/wiki/Market_maker
This is because sellers don't always want to wait around for buyers and vice versa.
Sellers that are worried they have poor market visibility can just put in a limit order that they believe represents a fair price.
There's no reason there needs to be a middleman here. Buyers can buy from sellers directly. In fact that's what they think they are doing, except that the HFT firms are basically adjusting the price on them underneath the sheets.
The real losers are the sellers. They put up some product at a price, someone else on the other side of town sees a slightly different price because the market only moves at the speed of light. Instead of the seller getting a little bonus, that bonus is hoovered up by the HFT guy in the middle who has a more accurate view of the market.
What service did the HFT provide? Where did this mysterious liquidity come from?
In the old days the middlemen were responsible for actually finding the guy making the sale and matching him up with the buyer. This was real work and it makes sense that people would be paid for it. Now the computer does it for you, there is no need for a middleman and no value he can offer. It's a parasitic relationship.