- Washington D.C. alone is all the EC BoS needs to survive. Yes, their defeat is a horrendous strike to their military power, but the population of Washington will make up for lost soldiers and they still have all the fancy tech they got by destroying and raiding various Enclave outposts. What is more, I am pretty sure that Maxson left an even larger army behind to defend their "homeland"
- if it is an easter egg because you can't get it without antagonizing the BoS, than the entire MM route is an easter egg because you can't get into it without antagonizing the Institute (unlike Railroad and BoS routes). The MM are YOUR army, that is why you can only get "Destroy Faction" quests with MM only if you become the enemy of the said factions (not to mention that MM are the only faction whose achievements are unrelated to the MQ)
The thing about BoS in Commonwealth is that nobody considers them welcome and if you tell the MM that you are going to destroy the BoS, they get all happy. Heck, I was surprised how happy some NPCs are if the Institute destroys them.
Because I still like Mr. House more than them ;P (although I like most of FO factions).
Family aspect of the story is a very major of the game's storyline and the Institute ending is the only pro-family ending. While arguably an evil end from ideological perspective, the Institute ending is the only good one from "blood is ticker than water" and the game does several time get out of its way to remind you of this.
Overall, I'd say all endings are story-wise fitting.
BoS are to Beth's Fallout what Empire is to TES.
Didn't bring much luck to the Empire.
There are many ways, yes. But they come with their downsides.
In any case, additional reasons why I think some of the major stuff will be canonized:
Beth canonized several things from FO3. While one could argue that "Enclave Destroyed" stuff was required (but then again, it is like you said: they actually could have made it work). Canonizing the fact that McCready was not sold into slavery was unnecessary however. Oh, and Sarah Lyons did not die at the Purifier, again something that could have been handled more ambiguously.
But most important of all, there was something major which they did not need to do, but actually went out of their way to do it: they canonized Legion's defeat in New Vegas, in a way that hints (although does not outright confirm) that NCR ending was the one canonized (though I still hold the stance that it doesn't outright confirm it). Seeing as events of WC do not matter AT ALL to EC, this was completely unnecessary.
What I am saying is: if nothing else, I expect they will confirm if the BoS won or got defeated.
In any case, while do act arrogant I also do try my best to explain my reasoning. If you don't like something I said (or if these points somehow insulted you), then do try to give actual arguments instead of personal attacks.
Have you tried a save where Tactical Thinking was never started? It is possible that the quest can't start because you already failed it.