What a strange interpretation to what I said.
The reigning premier remains so until a new premier is crowned. A home and away season win against the premier doesn't make that team the new premier (there would be a new premier every week if that were the case, including bottom 4 sides). They only become so when they win the premiership (It's also the same in your analogy - an imperial leader may lose battles or be away from his throne during his rulership but until there is a new imperial leader that takes over - his reign - and by extension the dynasty - remains). (Hell, extending the analogy of imperial dynasties further, multiple times there were separate dynasties by the same family. Once the dynasty was broken - it was no longer the same dynasty anymore - even when they came back to rule again. When they did so and a succession of rulership recurred, it became a dynasty again).
Same with your 8 premierships in 9 seasons example - that would be 'dynastic' for the period(s) they maintained the premiership. By virtue of those results they would at least have to have 1 (and likely 2) clear dynasties.
This is the problem with making up your mind X team has the best dynasty and only after you have decided this you start considering the facts. As we have seen from Fudge here, you need to start doing callisthenics with the facts presented by others in order to protect your position.
Fadge Better to simply say what the four teams achieved are all defined as dynasties by the thread question. Then you only have the Hawks extra flag, the fact they beat better performed finals teams in their Grand Finals, the facts Brisbane won finals in more consecutive years and had to overcome playing Grand Finals and other finals on their opponent’s home ground and the fact Richmond beat better performed finals teams in their Grand Finals to overcome in order to get the Cats out of the wooden spoon dynasty position, let alone get them to the top. Oh, and the Tigers like the Lions also did the opponent’s home venue Prelim-GF winning double in 2020, as the Gabba was Geelong’s preferred home ground at the time. Where the Tigers preferred ground was Metricon.
But against that I guess there is that the Cats were the best at winning home and away games at Pussy Paddock and had 27 genuine bona fide All Australian players in just one of their seasons alone.