Why do turbofan engines not have a contrarotating second fan?
The power to drive a fan through a gearbox is not beyond current technical capability. Pratt &amp; Whitney have developed the geared turbofan, the PW1000G that first ran in 2008 and entered commercial use in 2016, flying on 4 different aircraft, including the Airbus A320neo. This enables the fan to spin at a slower speed than the low pressure turbine, such that the turbine spins at a higher speed that is more efficient for power extraction from the relatively high velocity mass flow, while the fan spins at a lower speed that avoids the blade tips lossing efficiency or creating noise at take-off, due to near sonic flow. 

The engine design involves trade-offs. The complexity and weight of a counter rotating two stage fan needs to be balanced against the achievable pressure ratio with a single stage fan, and the added benefit a two stage fan would provide. Some design work has considered counter rotating compressors for example, this thesis. or even earlier work in  1992. The gas turbine industry can be quite conservative - it costs huge amounts of money, and time, to develop a new engine design, and radical steps are much less common than evolution. Pratt took a gamble, that appears to have paid off, though they do still have some issues. However, it took them decades, and around $10 billion. Rolls Royce are considering a similar design (the UltraFan), but GE are more wary. They have chosen the use of new materials as they felt the addition of the extra component would add reliability, weight, and durability challenges that they could avoid by using material improvements instead. For example, the use of ceramic matrix composites in the hot section of the CFM56 LEAP. They claim this gives 15% fuel savings, but has taken 25 years to develop. In comparison, P&amp;W claim the GTF is 16% more fuel efficent than current generation engines. So each manufacturer choses the route they are comfortable in, and may get to the same end point. 

In general, the desire has been to increase by-pass ratio, as this lowers specific fuel consumption. However, increasing BPR results in larger diameter fans, and higher tip speeds, approaching sonic velocity if the turbine is run at the optimum rpm. Hence, the geared fan approach. Clearly, Pratt &amp; Whitney did the trade-off analysis, and decided this was the best approach for a geared fan, balancing techncial risk, reliability, performance, in-service cost, and weight.