A canon ending is just an ending that is the one that is chosen to continue the narrative. Not that any of the current routes aren't capable of being declared canon, just that generally there isn't a declared ending when they are all so radically different. To put it another way, if in the Knights of the Old Republic game back in 2003 the Dark Side ending was declared the canon ending, it means that the following games and universe would treat it as such. That would obviously not be a "happy" ending, but just the ending.
So if they remade SS to be the canon ending and had Edelgard play the villain and have her die at the end, I would not consider that a happy ending, but it would be the canon one. Currently, the AM feels the closest to a canon ending because not all the other house leaders are killed.
Another example I just thought of is XCOM2, in which you lose the first game. The canon path of the current XCOM universe is that the player did not win in XCOM1.
That's why I would have advocated for a more nuanced route that combined them all, because almost all of the routes could have been combined if the leaders had talked to each other, because in general, none of their goals are even opposing. All want to destroy Those Who Slither in the Dark, intentionally or otherwise, all want a better future for Fódlan, and the issue between them all in their past hurts and their inability to trust others.
Even with a canon path I don't think you need to imply that the morality espoused there is per se the correct one. You could even have options where Byleth openly disagrees with the chosen path, but for moral or ethical reasons can't join the other side either. If you keep Edelgard the villain, Byleth may just find it more egregious to work with TWSitD than Rhea and crew despite them also being flawed.