[Gigachad]

I don't believe the limitations of physics are anywhere near what current drones sound like. They are loud because zero effort goes in to making them quiet. It's not so much the moving air that makes them loud, its the whining motors and bearings that are loud. If you were able to encase those motors inside and perhaps put some effort in to making the air stream less turbulent, they could be a lot quieter.

Although I still can't see drones being good for this even with good designs.

[dTal]

It is certainly not "whining motors and bearings" that makes them loud - it is the fact that you are creating massive periodic pressure differences with the blades. It is the same reason helicopters go thump-thump-thump, but scaled up in frequency. Have you ever heard a quiet propeller? About the best you can do is increase the size and decrease the speed (more efficient = less power dumped into the air), add more blades (minimizes circumferential pressure variation), and add a duct (eliminates tip vortices). But eventually you hit weight limits on all of that. At drone sizes, unless the drone is impossibly feather-light, you're always going to have some sort of whine.

Even in the absolute theoretical best case scenario of an idealized disk-shaped actuator inside a duct with proper lip shaping and 0 turbulence around the actuator, the shear boundary of the high velocity output plume is unavoidably going to cause turbulence. The best you can do is "woosh".