We always solve questions by drawing two tension forces at the diametrically opposite end, to show that tension is pulling the pulley, but from the research I have done, it is clear that it is not exactly the tension force but the summation of normal forces between rope and pulley that pulls it. Then why do we not use this in real life and put 2 arrows along opposite points of the pulley? And how can I prove that the summation of normal forces is actually equal to $2T$?
For simplicity, assume the pulley is not rotating but the rope is slipping on it and is massless (nearly) and frictionless, and that the rope also has negligible mass.
It would be great if you were able to clear my concepts.