Alright, I took a look at your file and there are a few issues at play here. Firstly, the 45 degree angle selection, the black chamfer artifacts, etc, can be fixed by disabling "optimize slice edges" in the tyBend modifier. That will preserve all slice geo without trying to minimize internal faces. The minimization algorithm is what's preventing those internal faces from welding together properly post-cut, and creating the artifacts.
As for the first couple images, your model is a very specific case whose solution can't really be generalized in the way you're requesting. On most models, welding within some threshold to the slice plane would create all kinds of other artifacts. It just happens to seem like a good solution here because your model is perfectly flat along one axis. So the work required to implementing a special welding algorithm for a single type of model doesn't really make sense. I think a better solution here is just to further subdivide your model prior to bending.
As a side note, it does seem like my slice optimization algorithm, which is creating the artifacts you noticed, is not working correctly in all cases. I will keep your file on hand to figure out why it's failing in those few cases where it's not cleaning up verts correctly, leading to the gaps between faces.
As for the first couple images, your model is a very specific case whose solution can't really be generalized in the way you're requesting. On most models, welding within some threshold to the slice plane would create all kinds of other artifacts. It just happens to seem like a good solution here because your model is perfectly flat along one axis. So the work required to implementing a special welding algorithm for a single type of model doesn't really make sense. I think a better solution here is just to further subdivide your model prior to bending.
As a side note, it does seem like my slice optimization algorithm, which is creating the artifacts you noticed, is not working correctly in all cases. I will keep your file on hand to figure out why it's failing in those few cases where it's not cleaning up verts correctly, leading to the gaps between faces.