Use this kind of phrase when you want to emphasize the person who did something. In the situation above, if you said:

You kept complaining about how old and ugly our TV was!

...then the focus of the sentence is on "how old and ugly..." This sentence is just an explanation for why you bought the TV.

But when you use "you're the one who...", it focuses the sentence on the other person. One use of this phrase is to put the blame for something on that person. When someone blames you for a problem, but you want to say it was their fault, use this phrase:

A: This place sucks!

B: You're the one who wanted to come here so badly!