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.