You could just stop by the Chrom read and maybe read the OP. Just saying. Pretty much everything you asked is answered there. And what? Robin's portion of Awakening's plot (the second Plegia/Grima arc) is the single most-often pointed to portion of the game when it comes to poor writing. General consensus pretty much everywhere is that the Chrom/Gangrel arc was the strongest of the Awakening arcs while the Robin/Validar/Grima stuff was plagued with dumb plot points.
Leaving aside Smash entirely (since I've literally never said Chrom was likely), this is absolutely wrong, actually. Chrom's character arc centers largely around the theme of fatherhood, which in itself is unique among lords. Sure, Eliwood and Hector would eventually become fathers, but not until after their journeys concluded. And Sigurd was a father but it happened far too late in his life for it to impact his character to a significant degree.
But for Chrom himself, the idea is a central pillar of his character. In chapter six he details the history between Ylisse and Plegia to Robin, explaining how his father, the previous exalt, led a crusade against Plegia to preemptively stomp out the Grimleal. The war ravaged both countries, and Ylisse was so low on troops that Chrom's father conscripted non-combatant farmers to essentially act as cannon fodder while he commanded from on high. The war ended with his death, leavin Emmeryn to rule and face the mess her father left behind, while acting as a sort of surrogate mother to Chrom. And considering the war coincided with Chrom's younger, formative years, it had a profound impact on him.
The atrocities his father committed inform many aspects of his character. Emmeryn instilled in him his good-hearted nature, but Chrom took it upon himself to protect his people. He formed the Shepherds out of what was essentially a group of his friends. He fought alongside them instead of commanding them, station as Prince be damned. And he cares for each and every last one of them as family, as shown in his Summer Scramble support with Stahl and several of Vaike's supports, for example. Even with Donnel's recruitment, he doesn't conscript Donnel the way his father would have: he inspires him, and Donnel volunteers after proving himself capable. In this regard, he is a father to his men, and a sharp contrast to his own father. And Chrom's major trait, being fiercely protective of those he loves, is a classically parental trait, emblematic of a father.
But then come the events of chapters nine and ten, and Chrom (spoiler alert) must cope with the loss of Emmeryn herself. After Robin leads the Group Pep Talk™ to get him back on his feet, he leads the charge against Gangrel and ends the war between Ylisse and Plegia, leading to an era of peace that lasted...two years. But in those two years between wars, something important happened: Lucina was born. As acting Exalt, Chrom is no longer just the father of his country, but a father in the literal sense. And now that the Valmese Empire is encroaching on Ylissean soil, Chrom has no choice but to fight back and secure a future for his daughter.
A lot of people say the Valm arc was kinda filler-y, but while it has its issues (namely a lot of telling over showing and handling Say'ri and Yen'fay haphazardly), it furthers Chrom's other arc, which was becoming a ruler worthy of his people. Chrom states during the initial visit to Regna Ferox that he was never much for diplomacy. Emmeryn's death, however, had an impact on him, and when it comes time to fight Walhart, he offers Walhart a shot at peace, extending the branch as Emmeryn would have. It doesn't work on Walhart, but Chrom is actually a tad remiss over it, even apologizing to Emm under his breath because diplomacy failed. Walhart further discusses this in his paralogue, setting apart the path of kings and conquerors.
Chrom's biggest revelation comes when he finds out that "Marth" is his daughter, Lucina, from a future where he fell in battle. His reaction is especially telling. "You deserved better from me than one sword and a world of troubles." This draws a distinct parallel between him and his late father, as his father left him and Emmeryn with the exact same things: Falchion for Chrom, and a world of troubles for Emmeryn. With his resolve further bolstered they're ready to take on Plegia, and when Robin finds out about his own heritage, Chrom tells him he's "his own man before he's anyone's son," further drawing parallels between Robin's paternal situation and his own. After all, Robin is just as much a part of Chrom's family as anyone else among the Shepherds, if not more so. Their bonds give him strength.
Chrom is far from a bland rehash of the series's previous lords. His tale, instead, is about fatherhood and its many forms. In a journey of self-discovery and his coming-for-age, Chrom becomes a father to his men, a father to his country, and a father to his own daughter, and, in the process, becomes the total antithesis of his own warmonger father, becoming a man and ruler of his own design. And in this, he became my favorite character in the franchise.
Just because a character arc isn't tossed in your face at any given moment, doesn't mean one doesn't exist.
