I think I have learned in physics that escape velocity is defined as the speed at which objects going ballistic in the opposite direction of the main gravitational force are able to finally overcome that force (assuming the simplest case with two directly opposing forces).
This means objects ballistically moving away from Earth slower than that velocity would never be able to escape and will finally fall back to Earth.
I have heard in many documentaries that this is the reason that spacecraft must accelerate to that velocity to get into deeper space at all.
However, as far as I understand it, spacecraft are not purely ballistic objects and could be controlled and accelerated step by step as needed, so why is it not possible to escape from Earth with lower speed and just "keep going", i.e. "accelerating" (exerting force) only to not come to a halt ?