I think you're right. I don't think there is really much of a void problem, N-body simulations using the best fit parameters from observations match the structure seen pretty well. Of course the match is never perfect, that just tells us we don't know everything!
I think there is a lot of confusion in the literature about exactly what constitutes a void. A void in an underdense region, but how underdense? Clusters, the other end of the non-linear growth spectrum are easier to understand, since you can see them, rather than seeing them by not seeing them. However even clusters are poorly understood on many levels. You get a problem with voids when one group defines a void one way when say matching to simulations, then another group defines it differently when looking at data, apparently uncovering a 'void problem'.
For instance, I can't remember the exact reference but there was a paper that found a void in (I think) the NVSS galaxy catalogue. This was widely reported in the media and described an empty region as being so many millions of light years across etc. LCDM models don't predict empty regions anywhere near that big, so there was hints of a problem. However, this 'void' was far from empty, there were plenty of galaxies seen within it, just far fewer galaxies than elsewhere. Counting galaxies is a very uncertain method for determining the mean underdensity of a large region since galaxy formation is not well enough understood.