Here is how I picture a plausible reason for the voids:

The creation of this universe is now thought to be the outgrowth of a collision of two 'branes' or 'universes' occupying a similar if not the same space time and space dimensions. This is not the big bang theory of a sigularity exploding but rather a collision of things like wrinkled moving sheets in the wind. The collision will happened at different regions at different times as each wrinkle and fold collide over a period of time, speed and different dimensions.

Seemiongly seperate areas of matter and anti matter would arise. Areas of dark matter and energy with opposite gravity characteristics may also arise. Einstein showed that an anti gravity component to the universe ought to exist (then changed his mind uch to his chagrin later in life)

This would allow for slightly different conditions to form different kinds of matter and energy in distinctly different areas.
IF an area of dark energy ((with the attribute of a gravity that pushed instead of pulled)) was predominant in one area it would repel itself from that area and move out pushing other material along with it.

poof - large areas of nothingness are left behind as the original dark energy moved away from is epicenter billions of years ago.

Here is the neat part to my hypothesis ***

As the dark mater moved out farther the universe as a whole will begin to accelerate outward faster and faster...

The universe is accelerating in its expansion!

We used to speak of a great attractor pulling huge clusters of galaxies but we might now more accurately say that they are being pushed by the great repeller.