This isn't true. HFTs are very active and profitable in markets where there are no rebates (some US stock exchanges and most dark pools, futures markets, most overseas exchanges). Even in markets where you have no fragmentation at all, you'll find HFT. The rebate just gets baked into how wide of a market you provide or how eager you are to pay the spread.

The main reason Reg NMS and Reg ATS drove a proliferation of HFT was breaking the NYSE specialist's monopoly on liquidity provision. Even before that companies like Tradebot where very active in Nasdaq stocks on various ECNs. Automated trading is simply cheaper and it drove manual market-makers out of business.

For sure, but I find ATS/Dark pools as bad overall for the health of the market. Open markets are fair. Dark liquidity isn't as fair unless you're one of the dark pool participants.

Note that I work for an electronic trading firm.