Why are the intersections "bad"?

From time to time, depending on the part, residues from the Intersection can appear. This only happens for your Nominal-Geometry STL-File as well as for your retransitioned NURBS-Geometry. The root cause is that you have enabled the automatic Non-Design growth. In this case, all Non-Design surfaces grow a little bit beyond their boundaries to ensure a trouble-free and clean intersection. This is done with an automatic detection of Non-Design faces. The left picture below shows such a case.

With the Advanced User Settings the automatic detection and growth of Non-Design faces can be enabled.

In case the automatic growth is disabled, be aware that you have to apply Interfaces on all functional surfaces to ensure sharp edges and functional surfaces after the intersection. When no extra material is needed for the post processing of the part a Machining Allowance of 0 mm should be added nonetheless to guarantee the functional surfaces.

How the automatic Non-Design growth influences the resulting geometry here.

Advanced User Settings Command:

automaticFunctionalFacesDetection.positiveNonDesignDirection=true