The reason we don't have shiny textured tyres, is because LFS sacrifices its looks in this regard for better physics - tyre deformation means that the tyres have to be generated in real time and as such they cannot be reflective. As for the tyre colour, you can change it by editing the appropriate DDS file.
I think the reason is rather that it's either a DX9 shader effect only (LFS runs DX8), or that Scawen simply hasn't bothered with such graphical details yet. I doubt tyre deformation is a problem here.
You can edit the shininess of the way light refracts off an object as far back as DX7, you dont need shaders for a shininess effect. It's a good suggestion, +1.
a) if they look brown, you are either using rally tyres or have the colours screwed up on your monitor
b) only new tyres would be shiny, so if done properly the effect wouldn't last long anyway - to be added with visual tyre wear