I think the reason has more to do with the Propeller (P) factor and the rudder corrections required to over come it. This effect does not arise from gyroscopic effects - it is an aerodynamic phenomenon.
Low airspeed and high angle of attack flight causes the blade descending on one side of the propeller disk to see a lower angle of attack than it sees when ascending on the opposite side of the propeller disk. The blade on the side seeing the higher angle of attack generates more thrust creating a torque about a roughly vertical axis. This torque twists the aircraft in yaw and must be resisted by a force created by a rudder deflection if steady flight is to be maintained.
High power propellers will produce a proportionately high torque about the vertical axis at high angles of attack and low airspeed. Thus, high power aircraft will require a significant rudder input to overcome this torque and keep the aircraft aligned with the relative airflow or the runway or to keep it traveling through the air in a straight line and on a constant heading. When operating at high power and low airspeed the required rudder input can be very considerable. A long climb can give a pilot one very tired leg. Also, on applying power by increasing engine rpm the pilot must also make a coordinated rudder input as the amount of rudder input depends on the speed of the propeller. Counter rotating propellers eliminate this P torque and any corrective rudder input requirement for changes in propeller rpm or aircraft angle of attack.
In addition, pitching and yawing an aircraft can change the angle of entry of air into the propeller disk. Once again, this can cause uneven thrust around the propeller disk creating a torque on the aircraft around some axis other than the one the pilot intended. This torque then requires yet another coordinated input from the pilot to maintain the desired flight path. The axes controls are said to be coupled and pilot inputs become complicated and non-obvious increasing pilot work load.
Finally, coupling of two axes in this way can cause an aircraft to continuously oscillate about the pitch and yaw axes and these oscillations can be out of phase causing the aircraft to continually vary pitch and yaw creating an uncomfortable sensation for those on board.
Counter rotating propellers can eliminate all the effects of P factor.
The inlet ducts of jet engines direct the airflow into the engine and the turbine disks and align it with the turbine shaft axis perpendicular to the plane of the blade disk.
As a result, P factor does not come into play here, jets do not have the problems caused by P factor, and jets do not need counter rotation to overcome it.