Why? That's not really a question of physics. A distant observer would see a a clock slow and light red shift on approach to a neutron star. Approach to a horizon is the same thing only more extreme. Asymptotically stopping just reflects that force needed to escape becomes infinite on approach to horizon. This stoppage is only observed by someone remaining further away from the horizon. There is no stoppage for the infaller.
I don't know what you are referring to in claiming I said escape velocities don't matter. I don't know what you are going on about traveling at or faster than the speed of light. I keep repeating this is all nonsense.
The singularity is a point in time not in space. Once inside the horizon, you can shine a flashlight any direction, and fire bullets in any direction, but all light and any projectiles you fire, in any direction, move forward in time toward the singularity. Poetically, you can say the singularity is a point in time where space ceases to exist for you. (In fact, you will be subject to enormous (ultimately infinite) compression and stretching, but you can always define a tiny enough region where everything is momentarily normal - until the moment of reaching the singularity).