Question Easy way to clean up "colinear" edges?

I'm not sure the best way to refer to this, but I'll call it "colinear" edges, because it's the existence of two edges in a PB object that overlap each other, but are not the same edge. I'm wondering if there's an easy way to automatically clean this stuff up.

For example, let's say I start with an object like this:



Then I delete the middle face:



And then extrude the left faces to cover that missing area:



The issue is the point I've circled. Even if I weld all the vertices in this object, it doesn't auto-split edges based on other verts being found along the edge. The result is that if I move long edge, we see it's not attached to the other two extruded edges, and results in gaps like this:



When this happens to me, I have to go around finding all of the "colinear" edges in my model, subdividing them, and trying to get rid of any colinear edges. That can be fairly time consuming. Is there any current way to "clean up" these colinear edges, such that the edges are automatically subdivided and then merged with other verts along the edge?