
Its not that simple. Cayden cant just say "oh yeah by the way alex has the blood of royal, thats why alex is my heir" and expect his people to celebrate it. The only reason no one go against cayden is because people believe the royal blood ended right before cayden claim the throne and they saw what's gonna happen if anyone who's not a royal going on war against him so they have no choice but to accept the fact that cayden is the only king of the country they can serve

If edna's real identity as eden comes out to public, who's gonna guarantee there's no rumor that the dukedom is cooking some plans to go against Cayden and that's why edna's territory going so strong so quickly? Or alex being the heir is because cayden got threatened by edna as she and her husband have protected cayden once? Or any wild rumors at all that can ruin peace in the country because why not make rumor as crazy as they can? With all corrupt nobles who wants to riot, edna can never be eden and no one can know about it
Yall realize that all of Alex's problem towards the nobles would disappear of Edna reveals that she was the former prince Eden? And that Alex basically has true royal blood.