A missile intercept for explosions or a kinetic destruction the relative velocity will be measured in kilometers per second.

A little nudge doesn't do much, it's still a satellite in a substantially similar orbit. Any sort of nudge requires intercept, go up there and match its velocity so you can grab it and push. And still you have to push on it a whole lot to make a meaningful difference. Spin it up? You'd have to do enough to exhaust it's fuel it uses to orient itself.

You're sort of saying if you can chuck an apple hitting a car on the highway, surely you can tow it away to get it off the road. They're significantly different problems.