I don't know if I can go so far as to say I hate TV Tropes, but I must confess I don't really get it. First of all, I don't really understand the difference between a trope and a cliche. At the very least, I think one is a subset of the other.
Secondly, I agree with you that the concept of defining and categorizing them seems weird to me. I think that one of the reasons TV has become such a huge part of our culture is that it was a quick way to create a common culture for a large, diverse country like the US. But part of the fun of that is that whatever references we all understand are just that...understanding amongst ourselves. We makes jokes about the "nosy next door neighbor" and we all know exactly the kind of character we're talking about. No one has to go look it up in a dictionary and see Gladys Kravitz's picture to understand. Or there's a plot where someone lies about knowing a celebrity, and a joke will be make about Bobby Brady and his dear family friend Joe Namath, and we'll all chuckle, cause we get it. It's not important or necessary to list every known example, it's just a touchpoint, and we laugh and tacitly acknowledge that we all know the cliche (yes, I said it), and we move on. It's not academia, it's television.