If we want to get technical, the king's direct descendants have always been the first in the succession line, often preceding the monarch's other relatives such as their siblings or cousins, etc. Unless the child in question were a girl in a patriarchal society, in which case, the throne would pass onto the closest male relative (even then, there were exceptions, such as the last members of the Tudor dynasty, Isabella II of Spain, and many others throughout history).
Having said that, it is extremely common and realistic for succession disagreements to evolve into straight-up crises and even wars. Especially if there's a lot at stake.
I'm going to be info-dumping a lot about Spanish history because that's the one I'm most familiar with, so bear with me for a second.
The thing is, whether the Osamodas or Amalia ascend to the Sadida throne is a matter of great political importance. Yet everyone save for Yugo and Amalia act as if Aurora being the rightful heir is a fact. When in truth, that's the kind of conflict that should create alliances and rivalries. In other words, there should be people, nations, really, that prefer Amalia as queen before Aurora.
Power as great as ruling an entire kingdom leads to great conflicts of interest. People from all over the world will prefer a certain candidate over the other because of family ties, similar policies, shared history or principles, because it will allow them to have a hand in controlling said territory...
For all intents and purposes, Amalia and Yugo should most definitely have allies that prefer them in the throne over Aurora!
Hell, this kind of unavoidable conflict has led to wars even when there was actually a designated heir, so I don't know why Amalia should just take it instead of rallying up allies to defend her claim.
1) The Visigoth rule ended in Spain with the arrival and subsequent conquest undertaken by the Muslims because a rejected candidate to the Visigoth throne summoned them to retrieve his supposed crown and it completely backfired on him.
2) Isabella I of Castille was the sister to King Henry IV, and she became Queen of Castille after going to war against her niece.
4) The Spanish Succession War happened because, even though Charles II had appointed an heir because he didn't have any children, the powers in Europe said "no, thanks" and still went to war over who should rule since a certain candidate would benefit one nation or another.
3) Spain's gone through several Carlist wars throughout the 19th Century because Ferdinand VII's brother Charles did not accept how he changed the law so his daughter Isabella II could become his rightful heir and rule.
More often than not, nobody gives a fuck over the king's actual wishes!
And you're telling me Amalia and Yugo can't have supporters who'll prefer to have them on the throne rather than the Osamodas????
Queen Astra's position as ruling queen, alongside the Eniripsa and Pandawa Queens, already implies that in the World of Twelve succession is not a right reserved solely to the men in a royal family. So Amalia was always a suitable candidate to succeed her brother, meaning, she should have even less people opposing her!
Although the real problem with this line from the webtoon is that it implies the Sheran Sharms have lost all relevance and Amalia is protesting the Corvus family trying to take over the Sadida Kingdom despite having no ties to it. When in truth, the existence of a tentative heir bearing the Sheran Sharm name is the very reason they have any claim to the throne at all.
The whole point is that it's not a harsh but wise summation; it's a contradiction, and a plain false one at that.