A non-economist wants to know: if liquidity is beneficial to our economy and liquidity is a function of time, how how does the time-benefit curve look as t approaches 0? I don't know if you can quantify the benefit and map this curve, but if you could I don't imagine it would scale to infinity as time approached zero.

Liquidity isn't a function of time, it is a function of relative time between the predators (arbitrageurs) and the prey (market makers). If the predators are much faster than the prey, liquidity will disappear since the market makers can't survive (their prices are too stale and they are getting taken advantage of). It has always been this way, even since Nathan Rothschild used carrier pigeons to get news of the Battle of Waterloo.