I would like to get rid of several edges by selecting them and hitting delete. I can assure you that if I deleted these edges I would be left with valid quads. What happens when I delete the edges is that it deletes the edges (but does not remove the vertices that I want gone also) and removes the faces that I want to keep. This is making my current work flow much slower.
If the edge is a part of that face, the face is going to be deleted. Kinda just how it is.
Seems the point of the delete edge only operation is to make only the edge no longer part of the face. Like I said, a valid quad would be remaining. Wish I knew how to write a tool that deleted the edge and then rebuilt the face to save me an extra step. Thanks for your help. It sounds like I have to deal with it and pray it gets added someday.
i believe the delete edge only function is to remove an edge and leave the verts behind. you can’t have a face without edges and you cant have an edge without verts. a quad has 4 verts and 4 edges the face is just the surface between it all.
People keep saying “you can’t have a face without edges” so I must not be explaining things very clearly. I am not trying to do anything that would take away the edges or vertices that the face needs to be a face. here is a picture of an example of what I am talking about. If the edge highlighted in yellow were simply deleted (along with it’s no longer needed vertices) you would still have 3 valid quads.
You’re expecting a result that isn’t what is going to happen, because you ARE removing the edges that define those current quads, and you’re keeping the vertices. You are then expecting it to fill in those square shapes, but the problem is, they don’t consist of 4 vertices, rather 5 for the outer sqaures, and 6 for the middle one; and thus aren’t quads. (and as Blender doesn’t support N-gons, it can’t fill in those shapes with one polygon)
In that example, you could just move the two vertices where that highlighted line intersects the horizontal lines to either side, so that they are on top of the vertices on the outer edges, then remove doubles.
The operation you want to use is X -> Erase -> Edge Loops … and not Erase -> Edge …
And in the future you might post an image with the operation you want to use … saves on time and argument 
Actually deleting the edge loop will delete the top and bottom vertices on the left side, resulting in a trapezoid.
In the example graphic given, 3Dnut can accomplish what he wants by selecting ONLY the middle edge, then hitting XKey > Edge Loop. Blender will rebuild the faces back to 3 stacked quads (to make explicit what tatsuyame has implied).
Sorry, in hindsight my question should have been this: “Is there anyway in Blender to delete extraneous vertices when deleting edges, so that undesired face deletion does not occur?”
Right on! That is a good workaround for the problem that I was facing. I really appreciate your help with that. I knew there had to be a way to delete an edge AND have the extraneous vertices get deleted without killing the face or deforming the mesh.
Now it’s called X → Dissolve Edges …