> After a binarization to make the edge stand out ...

Edge binarization is dependent upon edge detection algorithm choice, threshold algorithm choice, and both of their respective parameters. It's often very difficult to find a set of parameters that aren't brittle due to occlusions, poor contrast, camera noise, etc.

Hough works great if you can do this part confidently. But in my experience, robust edge binarization for Hough is often not very feasible in the wild.