remember that in turbines the design point is sufficient airflow and
pressure ratios for combustion.  Non-turbine applications are effectively
super high bypass and the design driven by the airflow needs of the
duct/shroud.

George Wright

George,
Please tell me if I'm wrong but I seem to remember that efficiency of boat
props improved with an integral shroud i.e. the shroud is attached to the
prop and turns with the prop. That to my mind indicates that the inefficient
encountered because of the gap between the prop and shroud can be
eliminated - perhaps a shroud within a shroud arrangement would be an
improvement.

Of course this brings up problems with centrifugal forces because of the
weight of the rotating inside shroud. To my mind this could be solved with a
bearing/ guide arrangement between the inside and outside shroud.

I remember discussing this with Perry Mick and he was of a similar mind,
however he couldn't at the time envisage how he could contain the
centrifugal forces.
It would be an interesting exercise, I wonder if NASA has looked at this.
George ( down under)

There is no free lunch. The rotating shroud has skin
friction which would cause very high HP losses
at near sonic speeds.