Could a shrouded fan blade with long chord length be efficient?
The main objective of the engine is to generate required power $\text{P}$, which is:

$$\text{F} \times \frac{D}{T}$$

where $F$ is force, $D$ is distance, and $T$ is time.

Power generated by modern jets through continuous combustion of fuel dwarfs their piston predecessors.

Next up is efficiency. As in wings, longer, thinner blades do a better job converting this power. A typical measurement is the thrust-specific fuel consumption:

$$\frac{g}{(s \cdot kN)}$$

which is fuel flow (fuel over time) per thrust.

Piston engines went from 2 to 3 to 4 blades, enabling more thrust output, but the "wake", or turbulence generated from one blade lowers the efficiency of the next one following it. 1 blade is most efficient, but to get more thrust from the more powerful engines, some efficiency is sacrificed. Fan jets follow this trend with many blades.

But short blades with a very long chord would be hopelessly inefficient for generating thrust in air. A very good example of this thinking is the modern windmill design, with fewer, longer blades than the old style mills. The faster you turn, the more you want to be like the modern mill. The turboprop makes the most of propeller efficiency and turbine power but:

All types of props or ducted fans reach a speed limit where their own drag makes them less efficient than low bypass turbojets. Propellers reach this limit before fans do, which is why we see fans on longer range airliners.

So we did not get to noise reduction with this concept, which is relegated to desk top fans.

Modern jets do have some success with noise reduction by controlling their fan blade tip speeds, and by improving the design of their containment housings (nacelles).