SPOILERS!!!!
Since the show caught up with the books now, things are going to diverge a little lore-wise. In the books, the Starks are in a very good position. Jon's murder is not confirmed, he may very well be alive when Winds of Winter comes around. Bran's in the weirwood tree surrounded by the three-eyed crow and children of the forest, Rickon is safely stashed away in Skagos with Osha and Shaggydog. Arya's becoming less and less a Stark in Braavos, and Sansa is safe in The Vale acting as Petr's bastarddaughter. It is really only Ned, Cat, and Rob who are dead. This is close in the show, but with some people having different locations and such. As with the Karstarks, they've became a separate cadet house so long ago, I doubt there's very much Stark blood left in them to be really named Starks. They can very well claim their house's starter was a Stark, but if we want to go that route, Dany is a Martell as well.
The Baratheons are another thing altogether. When the series started (Books and show) they were never in a good position. Robert had no trueborn sons, Stannis only had Shireen and many more stillborn, and Renly was only beginning his sexual maturity. So far he's only had relationships with men so he's produced no bastards or sons that we know of. His early death men the Baratheons took a major blow in terms of lineage survival. In the show however, there are no Baratheons left. With Shireen's sacrifice, Sylese's suicide, and Stannis' apparent death at the hands of Brienne, the only real Baratheon we know of is Gendry, who will probably never surface again once his part was finished on Dragonstone.
To be fair and frank with you, the "good" guys in this series are getting screwed over heavily, and to quote
https://www.youtube.com/watch?v=ZXSSBu9uKrM, "George R.R. Martin, why are you such a sadistic bastard?"