The impact of such regulation was tested by the SEC recently with the 'tick size' program. Instead of reducing the minimum increment, some names saw it increased to $0.05. The hope was to increase liquidity while decreasing volatility in these names. In fact, those names experienced decreased liquidity with no decrease in volatility.
HFT is a result of regulation.
[0] https://www.sec.gov/divisions/marketreg/subpenny612faq.htm
[1] https://www.benzinga.com/general/education/18/04/11517027/th...