Non-metals always have a bit of specular reflection (usually in the 3-4% range). Most PBR shaders using the metallic workflow uses that fact and set the specular reflection for non metals to a constant value (usually 4%). Some use an additional greyscale texture to modulate that value (Designer's Metal/Rough shader call it the SpecularLevel channel).
In any case, you should not have 0% specular reflection if you want to be physically realist. The spec/gloss workflow allows it but it is not physically accurate.
The specular texture you get after conversion with the "metal->spec/gloss" is a uniform 20% grey because it is in sRGB (20% sRGB corresponds to 4% linear).