Sketch Doctor complains if non-construction lines and construction lines overlap. That seems wrong. The whole point of construction lines is that you're usually going to put something on top of them. Construction geometry should be viewed as a background layer on top of which one draws part geometry.
I'd suggest that such overlaps be considered errors in Sketch Doctor only if the entire construction geometry line is hidden by another line. If part of the construction geometry line is still visible, it's doing its job, and is not an error.
Related to this, when selecting coincident construction and non-construction lines, selection should pick non-construction lines first. This would make Close Loop operations much easier.
These changes would keep construction geometry from getting in the way of other work.