I'm not trying to be a jerk here, but I am going to be fairly dry. I like to be amiable, but you talked smack on the last person to reply to this; whether or not he is wrong (I don't really think he was), being a jerk does not merit being treated amiably.
Onto it…
Even at an epistemic level, this makes no sense. In other words, let's say you actually meant it is just a way for the WG to categorize pirates...
First: The WG doesn't "title" the Yonko. The Yonko seem to be determined simply by world-wide perception of them, which includes the perception of all persons as well as people associated with the WG. So, again, the WG does not decide who is considered a Yonko, though they might have some insight into who the strongest pirates around are. They do not "name" or "title" Yonko; at best they just acknowledge when a pirate is considered by the global (or perhaps just grand line) population to be a Yonko.
Second: Yonko will be "replaced" only if people - not the WG - start referring to some pirate or other as "Yonko." It is likely that is Luffy takes down Kaido, people might start calling Luffy an emperor; this has very little to do with what the WG has to say.
Third: You're probably right that the WG uses this system to categorize the Grand Line, but only because this "system" is already in place - people call some pirates or other Yonko, and the WG keeps track of this. They don't manipulate it in any way - they probably couldn't, since that involves directly engaging/directing the most powerful pirates around - they just take note of who is recognized by the world (not to be confused with the world government) as Yonko.
Fourth: If the system is just a way of recognizing the most powerful pirates around, the only way for it to crumble would be if there was no longer any point in the classification. It doesn't fall simply because 2 of them are defeated - that just means 2 people who were on top aren't any more. It only falls if there are no pirates worth calling emperors, or if there are so many that the special name loses its meaning (if territory is scattered amongst a ton of pirates, then no one could be said to really have an "empire"). Maybe there are other conditions, but none of them have to do with the government's say-so.
Yonko = Emperors. It just refers to Pirates with significant strength and territory. Consider it to be somewhat like a country. Sure the WG could refuse to acknowledge some country or other (just like many countries do in real life), but that doesn't make the thing people call a country any less real.
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Just to bring you in here, I more or less agree.
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Oh, and: Your example is awesome. The gorosei don't get to decide who a Yonko is. Marco and BB are the likely pirates to take Whitebeard's territory, thus acquiring his "empire," and thus having the best shot at being called an emperor. They do have insight, since they were right that it would be either Marco or BB, but they don't name or title anyone. The term "system" is super misleading, since it really is just what people (generally - not specifically WG) call pirates with territory and strength. It's just various people being called the same thing with no real structure to it other than some properties and relations pertaining to the individuals themselves named Yonko.
