Here’s a scatterplot of near-Earth comets (data source: NASA).
We see that orbits with small eccentricity tend to lie close to the ecliptic, while more eccentric orbits seem to lie on random planes (see diagram for terminology). This could be because the more eccentric objects were captured, whereas the others formed with the Solar System. Another hint that this is the case: inclination is not only closer to zero, but also note the absence of dots near 180 degrees, so they’re orbiting in the same direction as all the planets.
After I plotted this I noticed a bunch of points that seemed to lie on a straight line in this space (red dots). Checking the data showed that these are fragments of Schwassmann-Wachmann 3, a comet that is disintegrating. It’s interesting what a visualization can reveal: before plotting this I’d never heard of this comet. I suspect a simple model of disintegration will explain it.
I’d like to come back to this someday.