It turns out that Unity’s LineRenderer looks very bad when it’s close to the camera, especially in VR. It is not very convincing when you see it trying to align with the camera’s point of view.
This motivated me to create a new LineRenderer, which renders a cylindrical mesh:
The code for the cylindrical LineRenderer is available here.
The interface is very similar to the interface of the LineRenderer. Simply call SetPositions or set them in the inspector.
If you find any errors or have suggestions for improvements, please let me know :-)