To achieve seamless tiling with GL_CLAMP, you load the border texels with the just-inside-the border texels of the adjacent texture tiles. This allows the filtering sampling logic to work as if it were sampling from the adjacent tile.
Even better, you can pull this trick across all mipmap levels and is works perfectly because the 0…1 texture coordinates are always “just inside” the border texels.
This is effectively exactly what seamless cube map does. But the cube map logic is simpler because you don’t have to explicitly specify the border texels. They are implicitly defined by the edges of the other faces of the cube.
Although you can treat the outer ring of a non-bordered texture as a pseudo-border, by shrink your texture coordinates inward, this doesn’t work right for other mipmap levels, because the texture coordinates are not right.
I’m not saying you couldn’t use GL_CLAMP for other purposes (after all, nobody is forcing you to define the border texels that way). But you can’t get that seamless tiling effect across all mipmap levels with any other standard texture wrap mode.
Really GL_CLAMP was ingeniously designed – but apparently it solved a problem that didn’t need solving for most video games. [Edit: except for skyboxes :)].