Taking the study at face value, it only says that competition among HFT is bad. It also specifically admits that "As market-makers, they can update their price quotes fast when news arrives and provide liquidity to the market. In this case, the low-frequency traders in the market – the investors – benefit from lower transaction costs". In other words, at best it's advocating for some sort of monopoly for HFT, rather than getting rid of HFTs entirely.
Conclusions and policy implications
To return to our initial question: does stock market liquidity deteriorate when HFTs compete? The results suggest that competition among HFTs increases speculative high-frequency trades, which could lead to a deterioration in market liquidity.