The Romans don't like ambiguous situations. They hate power vacuums. If there's one thing their history has taught them, it's that the lack of secure leadership leads to civil wars or, horror, having an Emperor.
Therefore, it is understandable that Jason's disappearance makes everyone want to fill that void immediately.
Of course, Jason is important for camp. But it's even more important not to risk Reyna or someone else taking absolute power.
Reyna is under pressure. It is she who continues to refuse to have another praetor chosen. She is convinced that Jason is alive - on what evidence, who knows, - and even if the fifth cohort tells her to be more flexible, she does not give in.
Jason wouldn't do it in her place; why would she do it? Unfortunately, Octavian and the Senate are very vocal about it, and rumours are circulating about his possible responsibility for Jason's disappearance (circulated by Octavian or one of his lackeys) and her ambition for power. Of course Reyna is ambitious. She is a Roman. But she certainly does not aspire to absolute domination! What a headache!
But rumours are a problem, and she has to have her hands free to keep looking for Jason. Thankfully, demigods have a long line of stories to draw inspiration from. And what did Penelope do to prevent her from being given a new husband?
Reyna: So, if you want to become a preator, you must [insert very dangerous and impossible task to do]. If you do it, you will be the new preator. Octavian: This is absurd! You can't do it! Reyna: Why not? No rule prohibits it. Octavian: No, but... Reyna: Man up, Octavian. If you want to become praetor, you have to work for it.
