There is indeed a benefit in flying more slowly, but the aircraft needs to be designed that way to profit from slower speeds. You can see that wing sweep has been slightly reduced in the more modern airliners, but this is also due to better airfoils with higher Mach drag rise onset.
But some things will also cost more when you slow down: You have to pay the crew for more hours, and the aircraft cannot be utilized as often. To transport the same number of passengers requires more aircraft when they fly at a lower speed. The cost versus speed relationship is not linear, but it should have a minimum somewhere below today's operating points. Aircraft with a slower design cruise speed can be lighter and smaller for the same payload, but for now airlines don't have a choice of slow or fast jets; all manufacturers try to design their long-range airplanes for at least Mach 0.83.
This has a lot to do with marketing: The aircraft with the higher speed will show a shorter travel time for the same distance, so it will show up first in the booking systems of travel agents. Of course, now you will argue that most people book on the internet and will try to get the lowest cost, regardless of travel time. True. But this is not the sort of customer the airlines are after. Their profit comes from people in First and Business class, and these still book predominantly via travel agents. Therefore, Airbus and Boeing try to market their planes as the ones which come first on the Amadeus and Sabre screens.
If you would single-mindedly optimize a configuration for the best fuel efficiency, you would arrive at something close to the MIT D8 design or Boeing's SUGAR study. Note that both are designed to fly quite a bit slower than current airliners at Mach 0.72. These designs are for a world in which fuel costs 200 USD per barrel or more, while the current designs are based on the expected prices at the time of their design start.
When fuel prices were low, the optimum speed for the best transport performance was indeed above Mach 1. The Vickers VC-10 of 1964 sported a maximum cruise Mach number of 0.886 and still holds the record for the fastest commercial Atlantic crossing. When Concorde was developed, the general consensus was that future air travel would be supersonic. Only the jump in oil prices after the 1973 oil crisis put those plans to rest. Large business jets today can cruise at up to Mach 0.935 because their owners are less concerned with saving money by flying more slowly. Technically, there is still room for cruising above Mach 0.85; it's economics that keeps airliners back.
If airplane companies were free to pick the optimum Mach number, they would today choose a speed between Mach 0.78 and 0.82 with fuel prices around 50 USD per barrel. Note that this is the design Mach number range for regional jets which fly short hops in which the increase in trip time from the reduced speed is insignificant. Also, especially in times of high fuel prices airlines operate their gear at lower speeds in order to conserve fuel. But if you follow this link, you will learn that airplane companies don't have that freedom.
Drag does not go up with the square of speed. When plotted over speed, the drag of an airplane will first go down, reach a minimum and only then go up. Airliners fly close to this minimum, and they fly high to shift this minimum to the highest possible flight Mach number. They do this by flying in less dense air, which requires to fly at an altitude around 30.000 - 40.000 ft. An additional benefit to flying this high is the lower air temperature which makes the engines more efficient.