What exactly do eggcrates do to light?
Here is a video that shows a series of effects from no Egg Crates® to 60°, 50°, 40°, 30°, and finally 20°.

The answer is that up to a certain ratio of subject size and distance from the lighting source, Egg Crates make a light source more directional (harder shadows) while also allowing you to maintain a larger source (which offers the benefits of diffusion within the beam spread range).  Beyond a certain ratio (i.e., a small subject far away from the light source), Egg Crates have no meaningful effect because the subject fits entirely within the clear aperture of every cell in the matrix.  In that case the Egg Crate's only function is to reduce the overall lighting intensity just the same way a scrim does.

Another way to think about the effect is to imagine that each cell gives you a mini light source that has a certain beam spread angle.  A single, 2" light source with a 20° beam spread gives a light cone that is D*tan 20° + 2" where D is distance to the subject from the light source.  At 5' (60"), that computes to about 22", but it also has a lot of falloff from the center of its beam (fully illuminated) to its edge (dark because all light eventually eclipsed).  Now imagine that the 22" light circle is subdivided into an 11x11 grid of 2" squares at the subject.  Across the north-south and also east-west axis, the squares go from least illuminated (at the edge) to most illuminated (in the center) and back again, because the square in the center gets fully un-eclipsed light, whereas each square away from the center "sees" an increasingly eclipsed source.  Squares that are within the 11x11 grid but outside the radius of the 11-grid diameter circle are completely un-illuminated because they are fully eclipsed.  If you then created an 11x11 grid of 2" sources at the source, each square around the center would add its percentage of light to each square within the original 11x11 grid defined for the subject area, and the sum of all those squares is--equally illuminated within the 11x11 grid.  Around that 11x11 grid at the subject will be a fall-off pattern that is linear along the edges and circular at the corners.  A 48"x48" Egg Crate gives a 48"x48" area of even illumination 60" away, again with linear fall-off along its longer edges and quadradic fall-off around its farther-out corners.