Although I think the SEC has generally done a good job in terms of market microstructure (especially in terms of resisting ill-informed populist rhetoric), I really wish they'd start exploring sub-penny tick sizes, at the very least on the most liquid low-priced stocks.
Since decimalization, it's been two decades since we've had a tick size reduction in US equities. When certain stocks sit at a one penny bid-ask spread all day, that's a sign that penny ticks are too economically wide. It's consumers and ordinary investors that pay the cost in terms of higher spreads.
You can think of the bid-ask spread as the cost of liquidity. It's how much more you pay for immediate execution. The tick size therefore acts like a price floor on the cost of liquidity. Why are we imposing a price floor, one that's much higher than the free market price, on end-consumers? If we reduced tick sizes from $0.01 to $0.001, the cost of trading for most retail investors on most stocks would fall by 50% or more.
It blunts the price discovery process. It incentives HFTs to compete in an arms race of speed to capture queue position, rather than provide better prices. The only group it really benefits are the incumbent exchanges (who can avoid competing with new entrants offering better pricing), and large, active portfolios, like hedge funds, that incur high market impact costs.