It gets a little complicated: do you want to continuously display market data and only clear trades once a second, effectively having a visible two-sided auction once a second? Or should it not be visible? (In which case you're no longer giving market data to all market participants, something they'd rather see)?

There are a couple of large firms that make 5-6 figures a day from arbitraging the closing cross. I'm sure they'd love to run their strategies all day; whether they would make more money than HFTs make now is anybody's guess.