But the House of Mogh was completely taboo ever since Worf's father was blamed for - whatever it was he supposedly did. Or am I remembering that incorrectly?
The impression I always got was that a Klingon house consists of: a) immediate/extended family and b) loyal retainers. As far as I remember, Kurn is supposed to be the only family Worf has left in the Empire.
And if the House officially didn't exist all that time, wouldn't the loyal retainers have gone off to join some other House whose honour was actually intact?
I suppose I don't quite understand how the Klingon House system is supposed to work. Another confusing case is the House of Martok: Worf describes it as having a highly honorable reputation, Martok's wife is even supposedly descended from an ancient Klingon princess, yet Martok himself is supposed to be a 'common soldier from the Ketha lowlands' with no noble blood. (I think that was the phrasing used)
Alright, first to House of Martok. It is the House of Martok, but only now. It could have accumulated its honorable reputation long before it become the House of Martok. My take is that he married into the House.
Next to the Klingon political system. We know that it is a feudal one. So what you would consider a House are only the core part, the actual "aristocrats". Everybody else is probably bound to the land/place/stature in life.
At the time when nobody was in charge/Worf was excommunicated: the vassal Houses grew at the cost of the House of Mogh. But I would say that the average Klingon is not interested as to who is currently in power.
I will try to find the best, most similar example from our history. But in the meantime, maybe, you could find the best analogue in the video game Crusader Kings 1 and/or 2, I think.