Why are contra-rotating jet engines so rare? Why are contra-rotating jet engines so rare? Such a jet engine would have contra-rotating turbines, or contra-rotating compressors, or both.

In fact I cannot think of even one aircraft that has this. If some prop-engines have contra-rotators, I don't see why some jets don't have it either.

It seems to me the contra-rotating parts would be more efficient in extracting power or compressing air. There are already contra-rotating turboprobs (Tu-95), and turboprops are very similar to jet engines, so I think it is not a question of technical knowledge. Another benefit would be reduced or eliminated gyroscopic forces hampering yaw or pitch torque, which I will ask another question about.

BTW, I am considering axial-flow jet engines only. I totally forgot there used to be centrifugally compressed jet engines, which have all but disappeared.

EDIT: The question is about jets (either turbofans or turbojets), but I mentioned the Tu-95 and its turboprop engines because turboprop spools are very similar to jet engines. However, I thought those Tu-95 engines had contra-rotating everything, but it turned out only the propellers were contra-rotating, not the turbines. Nevertheless, if there was a turboprop with contra-rotating spools, I would very much like to hear about it here because I think it would have great bearing on the question of contra-rotating jet engines and their efficiency.
If the low-speed and high-speed spool rotate in the same direction, the relative speed between them is low. Contra-rotating means you need to double the individual speeds to arrive at the relative speed, and this will increase bearing losses greatly. Both friction and wear will go up with little benefit in regular operation. A notable exception is the Rolls-Royce Pegasus engine for the Harrier jump jet.

Stators between the rotating stages ensure that air flow inside the engine is mainly in axial direction, so aerodynamically a different rotation direction between two spools will make little difference. However, contra-rotation will indeed make the stator between the last stage of the high- and the first stage of the low-pressure turbine obsolete. The video linked by @Moo cites a 10% reduction in part count as the advantage. Additionally, the first stage of the low-pressure turbine should show improved efficiency (like the second propeller of a contra-rotating propeller).