most of the problems come up because Region and Voronoi3D want Boxes as region:
a Box is a box (nice sentence lol) while the Brep you are working with is not a box:
up to this point it’s good, you have removed from the random points all the ones that were generated outside your real Brep shape:
but in the next step, by non providing a Box that determines how big the Voronoi3D must be, the Component will generate a Voronoi that is just as big as the Bounding box of all the Points involved in the operation, which -of course- happens to be smaller than your initial Brep:
and when you do the Solid Intersection of the Voronoi cells with your initial Brep, the problem of having a Voronoi Box smaller than the initial Brep is still present:
when you input a non-box Brep into an input that wants a Box, GH will generate the bounding box of that brep for you, and use that bounding box to do whatever the component needed that input for:
so if you plug your initial Brep to the Box input of the Voronoi3D you solve the problem with just one wire:
all this long explanation was just to mention that probably all the straight edges that you would like to delete, are the edges of the Voronoi3D cells that overlap the initial Brep edges, similarly to this post (where I’d go with Laurent’s solution):
4rhinoforums_Re.gh (25.2 KB)
[edit] depending on the Populate3D seed you are using, there will probably be some locations in the Multipipe that appear like this:
that is because of some very short segments that create edges you might want to delete:
what I usually do is using Pufferfish Cull Duplicates because for some reason I really do like the Average feature… but that component can be swapped with remove Duplicate Points that comes with Kangaroo 2:
final result 
4rhinoforums_Re2.gh (31.9 KB)