we have dot3 shaders built in
No we don't. If we did, you could actually make stuff which looks as good as your demo but runs at practically the same speed as normal mesh rendering. What we have is a blend mode which can kind of make things look vaguely bumpy with a lot of fiddling and generally making things quite a lot slower.
Why does specular make everything look like it's covered in shiny plastic.
Because that's what specular is? Only polished surfaces such as plastic, glass and some metals exhibit specular reflection.
If you really mean why is specular used where it wouldn't naturally be, then the answer is because it's the most obvious way to show off your bumpiness. After you've gone to the trouble of writing nice bump/normal/parallax mapping, the last thing you want is for people to barely notice. So it gets overused. Full color specular maps make a big difference here and can create much more convincing representations of surfaces like wood, dull metals and skin. But having to use a full color specular map adds another texture lookup and another texture bind ( you're already doing at least two, probably three or four with shadows and other effects ) so it often gets left out, sadly. Greyscale specular maps can be implemented without the extra texture bind, because they can be placed in the alpha channel of the normal map. But they don't look as good.