My own impression is that the status of a House depends on a lot. Party of this is raw prestige. Mogh was evidently a famous man in his own right, while his father was a very prominent person as well. In theory, all kinds of debts of honor might be owed to the children of Mogh, as well as who-knows-how-much property. Worf simply had no particular reason to call upon those.
But internal evidence suggests Kurn had achieved some real status of his own, while his parentage remained unknown. Once it was revealed Kurn--a man Gowron knew and realized as someone important in his own right--was in fact the long lost second son of the great and revered Mogh, then Kurn's status soared to new heights. Nor did it hurt that when civil war broke out, Kurn supported the winning side.
We also don't know that much about Mogh's wife, who might have had considerable status of her own. Look at how Martok's wife helped him, because (in theory) she was the descendant of an Emperor.
Keep in mind, the House of Mogh didn't last that long as a Great House. By the end of DS9 Worf had been adopted into the House of Martok.