The tapes function similarly to the coin – they are substitutes for the real thing. Powerful substitutes yes, but still substitutes. At one point in the evening, Robert says to the narrator's wife, "This beats tapes, doesn't it?" (2.19). This connects with the narrator's admissions that his "idea of blindness came from the movies" (1.1), and that he's "never met, or personally know anyone who was blind" (1.31). Even though the tapes might seem closer to something real than the movies, neither one comes anywhere near the real thing. In "Cathedral" face to face, hand-to-hand contact is always the best.
There's also something rather ironic going on. The narrator is trying to show or describe something to the narrator which he's only (to our knowledge) only seen on television. The drawing of the cathedral is a copy of a copy of a copy. The narrator isn't even copying the cathedral he sees on television. He's drawing a cathedral from memory. Can Robert or the narrator experience a cathedral without touching/seeing one? Not precisely, and that's part of the point. What they need is to experience each other. They need warmth, and physical contact, the act of creating something together. And that is what's real. The story acknowledges that tapes, movies, and TV are important ways to communicate. Ultimately, "Cathedral" privileges face-to-face, and hand-to-hand contact as the most effective method of exchanging information.