How important was the "House" of a royal family to the public and aristocracy in British and/or European history?

by ryth

By the initial question I mean what was the reaction of the public and the elites to the house of a ruling family becoming extinct, or a new or different ruling house taking over, by peaceful means (i.e. marriage/birth of heir)?

Historically, I'd ask about the Stuarts being succeeded by the Hannovers upon the death of Queen Anne in Great Britain. A later example being the Hannovers being eclipsed by Saxe-Coburg-Gotha after Victoria?

Was the public really only concerned about the lineage of the new King or Queen, or was the house a concern?

It might also be interesting to hear about other countries in Europe as well.

Side question: The British Saxe-Coburg-Gotha branch was renamed to "Windsor" during the first world war, but would Prince Charles of Wales not be of House Battenberg now? Has this spawned two seperate new houses? Windsor (Saxe-Coburg-Gotha) and Windsor (Battenberg)?

Advokatus

Side question: The British Saxe-Coburg-Gotha branch was renamed to "Windsor" during the first world war, but would Prince Charles of Wales not be of House Battenberg now? Has this spawned two seperate new houses? Windsor (Saxe-Coburg-Gotha) and Windsor (Battenberg)?

Charles (like his father) is actually an agnate of the house of Schleswig-Holstein-Sonderburg-Glücksberg (which is a cadet branch of the house of Oldenburg).