Because that's how the math works. The equation that you use to determine gravitational force between two objects has the distance between them squared in the denominator, meaning that no matter how large you make it the value is never 0 (although it may be so infinitesimally small that for all intents and purposes it is nonexistent)

Imperceptible to the entity crossing the horizon emphatically does not mean that there are negligible or net zero forces acting on that entity.

If you had two hydrogen atoms separated by the width of the galaxy, they would still gravitationally influence each other.

What are you drawing that conclusion from?

You would pull up a cable with whatever probes or detectors you had attached to the end sheared off, with no data ever having been received from anything past the event horizon. Whatever signals you received as you approached the event horizon are also probably garbled beyond all comprehension; relativistic effects mean that for every second of time you experienced, the probe experienced orders of magnitude more. My guess would be that the data throughput on the cable would drop with the inverse square of the distance from the probe to the EH until it becomes functionally 0 (assuming you have a magical, radiation- and hot-matter-immune probe)