7km/s is "standing still" in low-Earth orbit.

Not if you're moving in a different direction. The opposite one, for instance.

The amount of delta-V required to orbit opposite of Earth's rotation is immense and very few projects have wasted the resources on it. I think most collision concerns come from inclinations and changing orbital altitude due to atmospheric drag. These are predictable effects, but it gets dicey quickly if your surface area increases because your vessel explodes.

It's not as rare as you might think. All sun-synchronous orbits are slightly retrograde (inclination = 98 degrees or so at 600 km) in order to take advantage of the precession caused by the earth's equatorial bulge and maintain the same local solar time in the ground track.

Also, Israel always launches in a retrograde orbit, since they have neighbors to the east who would react too well to what looks for all intents and purposes like a missile launch, or to expended rocket stages dropped on their heads. For that reason, Israel launches retrograde over the Mediterranean.

Even neglecting a retrograde orbit, though, just a slight difference in inclination is enough to totally ruin your day. Even if you're only off by one degree, if you're travelling at 7.8 km/s your closing perpendicular velocity at the node crossing is 7800*sin(1 degree) = 136 m/s. That's almost 500 km/h, plenty fast enough to ruin your day.