Anybody who starts off their paper with mentions of the Kardashev scale is already pretty far out there. It has never been clear to me if even a Level 1 civilization is practical, there could well be physical (as in physics based, like thermodynamics) limits that prevent you from reaching that point. And the scale goes dramatically up from there. Level 2 is building Dyson Spheres.
It always felt like the whole thing was made by someone who didn't really have a good grasp of scale. Maybe it's a failure of imagination on my part, but I tend to think that projects on scales like that are just too impractical for real life. It's like if you decided to make up a scale for land speed records, and made type 1 100,000 kph, level 2 100,000,000 kph, and level 3 100,000,000,000 kph.