Alright everyone is hammering the possession thing (which is alright) so how about this.
Let's say Rudolf is actively fighting his possession, so you get moments where he isn't possessed and moments where he is.
Yea possession was pretty dumb in fates but I think if done right it would be pretty interesting. If you don't like the idea that is completely fine.
So an Idea just happened: What if Rudolf's possession broke when he was wielding the Falchion to kill Mila. He didn't want to be possessed again so he put on a act. Rudolf while putting on an act was still trying to come up with a plan for Alm to kill Duma because he was stuck. So at this point any plan Rudolf made would be either rushed, not thought out, etc. Basically putting all his hopes on his son because he knows he can't defeat Duma (since he already tried). So ummm...Yea, how about that. I makes the possession only necessary to keep a civil war or coup or something horrid in Rigel to not happen so Rigel can later get in a war with Zofia.