For the black hole the ground is merely more dense vacuum, the ground has barely enough time to move if it comes in at interplanetary velocities (50km/s+), so by the time the ground will begin to react to the intense gravity, the black hole will have passed through with the force of a few hundred nuclear explosions.

Almost certainly not actually infinite in reality :)

We treat it that way because, despite it showing that our model of physics is breaking down at that point, it works really well for most real purposes. But look at string theory, loop quantum gravity, etc., and you will find plenty of the variants within those umbrellas do not have a singularity at the heart of black holes.