Maybe she's a little obsessed over Noctis because she loves him...? Did you guys forget about that? Luna is the Oracle of the world, she has a duty to protect the world, and knows that Noctis is also the key to saving the world. The prophesy fortells a day when the king will battle against the darkness and bring peace to the world. Everything that is done in Kingsglaive is for the future king, it's for the the sake of the people of the entire world. Without Noctis, the world will be plunged into darkness forevermore. When the world is in ruin and the skies are blackened, there is one person who can stop Niflheim, retake the crystal, reclaim his throne, and save the world from destruction.
I think that's a pretty good reason to be obsessed over him, especially when you're romantically in love with him.
I think that's a pretty good reason to be obsessed over him, especially when you're romantically in love with him.
Because that's what Luna feels like. Just a plot device.