The efficiency effect is more easily seen if you use the actuator disc analogy.
More solidity means you are accelerating the flow in the stream tube to a higher outflow velocity to get the extra thrust.
The work input is proportional to v^2*mass flow whereas the thrust output is proportional to v*mass flow.
To retain the same propulsive efficiency requires a bigger actuator disc and keep the same outflow velocity, but with a bigger mass of air.
This is the same reason that high bypass ratio turbo-fans are more efficient than low ratio ones