Something that really bothers me about the show is how all these legendary houses supposedly existed for thousands of years, yet when you look at the current situation a chunk of them are on the brink of extinction. I don't get it, are there no actual cousins to take over?
The Starks are all over the place with no suitable heir to take over, the leaders of house Martell are gone, the Baratheons are done unless you count Robert's ********, the last of the Arryns is a boy who was still sucking milk from his mother not too long ago, the Greyjoys are down to a dickless Theon and a lesbo Yara, not sure how their line is going to continue unless their uncle takes over, the Tyrells seem to be banking on their gay son to carry over yet with him being in jail the future is in jeopardy, house Tully looks done, and the last of the Targeryans is a female (Unless Jon is revealed as one). I suppose only the Lannisters seem to be somewhat in a better place, but even their situation is not that good.
I would imagine a future of a house is good if there was a lot of children, something like house Frey for example.