Just to point out here what's different between "space" and "not space": "Space" assumes no "height control",i.e. ways to exert force "down or up" along the earth-object direction. That's obviously not true for a plane. If you can exert force in that direction, you can change speed and keep the shape of the trajectory around earth constant.
They could. The point is that if you allow for that (and it they would need to be constant on), the more speed -> either higher orbit or more elliptic orbit doesn't hold. But no satellite has enough fuel to keep its thrusters on indefinitely.
