>>28608754
She can, but she then runs into a problem that was highlighted for vampires in the TES:V Dawnguard storyline.
Removing the sun, or otherwise obliterating it in Flan's case, would draw more attention to the Vampire(s). The masses would stop at nothing to reinstate order in the chaos bestown upon them through the selfishness of one (woman- Flan). Reimu and the others would be up in arms if the sun disappeared one day when it wasn't scheduled for an end for another few hundred million years. Without the sun, there are fewer to no trees meaning less oxygen.
No sun, no crops. That means less food.
No food. --> fewer humans.
Fewer humans --> Less food for the youkai. Humans dropping dead at an abnormal rate would directly effect the natural order of things in Gensokyo. Flan would be putting everyone in danger just to stop a single NEET. I know jokes about her mental state are often made, but that's the least educated thing she could do. Everyone would have their crosshairs on the SDM regardless of who it is directed toward because of her little stunt.
It wouldn't be in Flan's best interest to make the sun go pop, even if she can with relative ease. Besides, Sakuya can probably just rewind time and stop it from happening which nulls basically everything.