They come up in practice a LOT actually. The challenge with curve/curve intersections boils down to tolerances. Visualize two circles with different radii, with the smaller circle inside the larger circle, that meet at a single point. When understanding those circles as primitives (centerpoint, radius) finding that intersection point is relatively trivial. However when simply thinking of these as arbitrary curves, we have a condition where those curves are getting progressively closer together, but it's really hard to tell if they exactly touch, and exactly where.

Of course at a point we'll get close enough to consider there to be some intersection, but do we get "close enough" for a single point? for a portion of each of the curves? Does the result change with the scale of the circles? Does it scale when the relative radius between the circles changes? Making those kinds of judgement calls within the algorithms is really a challenge, but makes a huge difference when building a geometry library and for usability (for other developers, and end users). Knowing your use cases may be helpful in determining what's the right approach for these situations.