Why should a ducted fan/rotor not be capable of working in autorotation?
I never heard about that and cannot find a reason.

How could it? With a duct around it, would you not have to descend straight
down? And if you did, would the rotational mass of a rotor that small in

Straight down can be a possibility. But if you can fly the thing, you
can also tilt the thrust vectors. So just tilt it so that the airflow
matches airspeed like in a heli.

diameter, and designed to work at such a high rpm, store enough energy in
free fall, to stop your descent when you applied collective to land?

That's a design issue since it is not free fall. Otherwise it wouldn't
be autorotation. The rotors/fans would of course have a windmilling
braking effect. And certainly, the inertia has to be sufficient to allow
smooth and preferably save touchdown as should be the case in every
helicopter.

Smaller and faster rotors are less effective and therefore need more
descent rate (more power). That's fact, too. Compare the sink rate in
autorotation of a Hughes 500 and a R44 (or the HV diagrams).