The line length is the length that I want for the appearance I am seeking. It does help if I break the line into shorter segments by chopping it up with the Split Tool, but it really only makes the errors harder to notice. The Type does not have trouble rotating around the curve on a polygon.
The sample on the left is polyline with short split segments in the Line Type, the right is polygon with the same Line Type.
The line does match better, but at hard corners and around arc segments the line varies off the intended path.
Converting to Polygon is a viable workaround in a lot of situations but loses information, and it would seem to be appropriate to be able to use Line Styles on polylines and have them actually follow the path shape. It took me quite a bit of time to figure out that the problem was caused by the polyline. It isn't obvious that one should work and the other should not.