I think this should be implemented a bit differently, without the mesh conversion, and using the proper evaluated curves rather than the displist.
Basically. the proper way to do this is more like D13890, but using CurvesGeometry rather than CurveEval. At the moment, any code that uses DispList ignores the more recent developments for curves.
Also, in that patch we discussed not sharing a common "Edge" mode between meshes and curves.

Converting the curves to a mesh just because another object references the object in a modifier also seems unexpected from a user level-- it is visible change that will mean the curves aren't accessible in geometry nodes, etc.

I think you've missed that this is proof of concept. Waiting for an another patch to be accepted or implementing fully battle-proofed BVHTree and Shrinkwrap modules just to find out that the idea is not really useful for its initial intended use is not something you do in the early stages.

Also, in that patch we discussed not sharing a common "Edge" mode between meshes and curves.

I do not see such discussion. In fact, I do not see any discussion there.

it is visible change that will mean the curves aren't accessible in geometry nodes, etc.

I am not sure what you mean by visible change. Converting curve to mesh should not change the way the object is rendered, at all.