They might be OK over a few meters but longer than that they absorb too much light. In optic fiber networks they only use a narrow band of frequencies which doesn't lose much energy but over the whole spectrum the loss is too great.
Also there is the problem of threading hundreds of thousands of fibers to make the 3D invisibility effect which is a huge job.
One of the best ways may be to internal reflection but with a different medium. There are certain liquids that can be placed in tubes with a certain coating and the light stays in the tube, with internal reflection off the coating. This is much more efficient than mirroring a tube unless perfect mirrors are used. With liquids like this it might be possible to do a plane size though the liquids probably put absorption lines in the image.
High resolution is not needed on a plane for example. Each pixel might be say 10 centimeters in diameter, which would be hard to see a kilometer away. Since each tube feeding that pixel might be say 1 millimeter in diameter the internal tubes don't take up much room.
Personally I like the idea of wide angle lenses covering the plane and perfect mirror tubes though the radar absorption is a problem. One possible solution is embedding small magnets in the glass which should absorb the radar.