I am familiar with the usual derivation of the fact that it is impossible for someone to observe an object enter a black hole, because of the fact that light gets infinitely redshifted as its source gets closer and closer to the event horizon. But one thing that bothers me is when you think of the problem backwards: if I emit a photon from "infinitely" far away in the direction of the black hole, then when it gets to the event horizon it will be infinitely blueshifted from the perspective of a stationary observer just above the horizon. So it means that the measured energy for the photon will be infinite. My question, than, is whether this simple thought experiment has some implication regarding the geometry around the black hole (since this new energy would be a new source for curvature). I know this might be related to some formal problems regarding black hole scattering and things like that, but I would first like to hear a more conceptual take on this.
Edit: Someone has pointed this question as a possible duplicate of What will the universe look like for anyone falling into a black hole?, but I don't think that addresses exactly the point I am raising here: I am more interested in whether there would be room for a physical consequence caused by the blueshift that light suffers when approaching a black hole, regarding things like curvature etc.