Not sure how it works in that society, but Carl, Akira's father, ran away and gpt himself if not disowned then at least removed from the succession line - as a result that would most likely invalidate Akira's succession rights as well. And you must no forget that Akira himself is a citizen of another country - worse, he is a noble who governs territory there and he's a retainer of that county's crown princess. That's a lot to consider, making him the next heir of the Rainford family is not a trivial matter. So marriage might be a necessary justification under such circumstances.
He still has the family name as does his father, so disinheritance or removal doesn't seem to be likely.
And being a citizen of another nation should not be a problem, since his blood IS that of true nobility, that's easily traceable and recognizable by all royal families so far.
And we've seen with all the hero lines, blood is considered important when it comes to ancestry and from where someone hails.
Also, I don't think he is tied to any kingdom, else Medysfina's mother wouldn't push so hard to have Akira impregnate one of her daughters in order for him to get "tied"