The lines make it easier for the eye to track from one point to the next of the same series.

They also make it easy to visually compare different wear patterns for different species, especially as the teeth are sorted back-to-front. For instance, on the mandible chart, the lines make it very easy to see that the teal, red, and blue lines have similar patterns.

I agree that a stacked bar graph would be nice, since the focus is on the per-species total across all 8 tooth types.

Could you explain why a line graph is bad for a discrete but ordered variable, like [Molars - Premolars - Canines - Incisors]?

In this case a line graph is bad because the line doesn't mean anything. It implies an extrapolation that doesn't actually exist.

Stacked bar graph

Harder to read

Choice ultimately down to personal preference.

6 different overlapping lines like that make it easier to read? It's amazing what people chalk up to personal preference.

If you have a better hypothesis as to why the authors chose a line graph over a bar graph, I'm all ears.

In the meantime see comment upthread for a rationale[0]

[0]: https://news.ycombinator.com/item?id=14555853

I strongly agree with the other guy