A conventional propeller may be thought of a single-stage compressor rotor sans stator. If you were to conduct a tuft test, of a smoke-stream test, you'd find the slipstream is a vortex about the propeller-shaft axis. This vortex represents energy (static pressure) losses that can readily be recovered with either a stator assembly, or with a contra-rotating prop system.
But worse, if you tried to put a second prop in series, behind the first prop and turning the same direction, it would have difficulty achieving a similar pressure rise, because of the poor match (low alpha) between the airflow vector and the second prop blade angle. This is the situation you face in a statorless axial compressor.