Roughness Value of (Close to) Zero in Physically Based Rendering
Yes, I think it's expected that setting roughness = 0, combined with using point lights for illumination, leads to no visible specular highlight. The size of the highlight is infinitesimally small, so the sample points (e.g. pixel centers) almost surely miss it. The math breaks down as well, as the reflectance would become infinite on the zero-sized highlight (a delta function).

Clamping roughness to a minimum seems like a physically reasonable thing to do. 0.04 feels like too large a minimum, though; I might pick 0.001 or 0.0001 or something like that.

If you use area lights, then a perfect mirror surface (roughness = 0) could still work and would show the sharp reflected image of the area light. This would probably still require special-casing the perfect-mirror case in shading code, to avoid the problems with infinities.