It is true that from the perspective of an observer inside the event horizon of a black hole, the photons falling into the black hole would appear to be infinitely blueshifted and would arrive at the singularity at the center of the black hole all at the same time. This is a consequence of the extreme gravitational forces present in the region, which cause the photons to be blueshifted and to follow highly curved paths as they fall towards the singularity.
However, from the perspective of an observer outside the event horizon, the photons falling into the black hole would not be infinitely blueshifted, and would not all arrive at the same time. From this perspective, the photons would follow paths that are determined by the curvature of spacetime, which would generally not be straight lines.