The idea that reduced tick sizes would force traders to compete on price rather than time is a popular HN market microstructure solution, but it's wrong or at least partly wrong.
1) Liquidity taking strategies will still "compete on time" in order to trade at the most favorable prices. Market making strategies will still "compete on time" in order to avoid getting picked off.
2) Inverted fee venues and midpoint order types offer sophisticated traders the opportunity to trade at prices within a 1 penny spread. If you watch the tape for a stock like ZNGA you will see this type of trading.
3) There are a number of high priced / high volume stocks that don't trade at a penny spread. GOOG is a good example. Do you find GOOG trading to be somehow cheaper, more orderly or efficient than e.g. MSFT? The GOOG spread is almost never a penny and is regularly over 20 cents. If the benefits are there, they ought to be obvious.