Contra rotating props are mechanically complex and pose serious maintenance issues when used on piston engines, and tend to be very noisy. The advantages are counterbalancing of torque, and more thrust in a smaller space than a single prop. However, the rear prop will not have the smooth airflow the front prop encounters - it will be cutting into the pulsing airstream from the front prop, so additional stress is imposed.
Several military aircraft in the US tried them in the prototype stage but abandoned them when the drawbacks outweighed the advantages. These include the Northrop XB35, which had gone to single props in the YB35 production version, before the turbojet variant, the XB-49 eliminated propellers. The Hughes XF-11 abandoned contra rotating props in its final version. Another Northrop design with contra rotating props was the XP56, although its contra rotating props were but one of many problems that design had.
The Avro Shackleton, which was successful, was known for high maintenance on it's prop gears.
A notorious example was the XF84H"Thunderscreech", infamous for its very high noise levels... just like the TU-95. The advantages of contra rotating props were not found to outweigh the disadvantages.
Later western military turboprop designs, such as the Lockheed C130, dispensed with the complexity of contra rotating props in favor of better single prop design. Same is true of the Airbus A400 military transport - four single props.
Contra rotating props were part of the Unducted Fan design, which saw some use in the Soviet Union, but didn't prove to be advantageous enough to see commercial use in the US, due partially to high noise that would have had problems with noise restrictions at most western airports. Ironically, some of the prop blade tech developed for the GE CFM36 unducted fan was later used on the huge and highly successful GE90 turbofan.
In the end, the western nations solved the issue with the high bypass turbofan, which is equally efficient, capable of higher speeds, and produces far less noise.
If anything, the TU-95 stands as a testament to the Russian ability to build robust military platforms, and a testament to western tech to solve problems with a different design rather than brute force.