Ephraim's problem isn't that he doesn't belong in the game, his problem is that his character arc is underdeveloped and thus makes the relationship between the two imbalanced.
When you look at Eirika, while she has problems, there's a clear story with her. She's naïve and new to war, she undergoes trial after trial where her naivety is tested, and eventually she makes a mistakes that causes her to realize that she needs to grow from that and become a leader willing to make the sacrifices necessary to succeed for herself and her people.
Ephraim is supposed to be the opposite: He's cocky, brash, and jumps into battle without thinking, and he neglects his duties and doesn't think too far ahead, which leads to him being looked at more as a figurehead then a true king. Ideally, the story would be he'd realize his neglect and get punished for his brash mistakes, but aside from one case (which admittedly is notable since it's a major setback and forces him to change) it's not that acknowledged and barely pops up. Eirika makes more mistakes in her story that leads to the final one, Ephraim gets a pass aside from a couple moments, which lead to him looking more perfect.
This has happened with other lord groups, so this is more a problem with IS' writing then just the character, but it is more notable with him since the story more strongly stresses their duo story aspect. If he was more balanced, he'd be a better complimentary to Eirika, but as is it ends up being pretty lopsided.