This can be partially fixed with a very technocratic market microstructure change (eliminating the subpenny rule). But politically that's very much a "huh?" point - imagine Bernie Sanders saying "I believe we should let traders quote in increments of 1/100 of a cent, not 1 cent".
Eliminating the sub-penny rule would probably be counter-productive for most US equities. You would not see further spread compression (most stocks' natural spreads are already greater than one cent), and displayed size would likely shrink (this latter bit is exactly what happened when prices decimalized). A better alternative would be a tick-size schedule that's a function of price, as is generally done in Japan and Europe.
The "displayed size" would probably shrink, but so what? You'd just need to look at the book to see it.
Decimalization would help even with equities where the natural size > 1c. HFTs who want to get to the top of the book could compete by offering $10.0073 instead of racing to be the fastest at $10.0100. HFTs would compete on price rather than speed.
A more granular tick doesn't just "spread out" the existing liquidity to a bunch of price levels--it meaningfully decreases incentives to post serious size. The spread will end up being marginally tighter, but with thinner books, you still pay more to trade large amounts. The objective function to minimize is transaction costs, not spread.
Since then, we have additional data points from the decimalized US equity markets. See http://www.sec.gov/rules/other/2014/34-72460.pdf for a bibliography. The weight of the evidence points towards thinner books. Incidentally, the SEC is looking to increase the tick size for illiquid small-cap stocks for this very reason.