In regards to the idea that Robin is not "set-in-stone," I would argue that Robin is much more set-in-stone than the other avatar based characters we've seen so far; he already has a preset personality, backstory, and abilities. Because of that, I think of him as more of a customizable character than a true avatar. With a character like the Villager, that really is just meant to be a way to put yourself into the game; the character itself has no personality outside of what you give it through your actions and imagination. Robin, on the other hand, is not designed in a way that allows you to put yourself in his place. He has way too much of his own personality and prominence within the story for him to be an empty shell to put yourself in. So I think that gives him an edge as a character choice.
Also, I find it a little odd that you brush off Robin as "that avatar character you play as in a few games," when Chrom has only appeared in one. The avatar/tactician concept is one that has appeared in multiple Fire Emblem games, and while the way it's implemented changes from appearance to appearance, and while it may not be the face of the series (similar to the Pokemon Trainer), it still represents an integral part of the Fire Emblem series that, I think, deserves some recognition in Smash.