Ah, I have to correct you. If you look at the scene again, you'll see that Celestia didn't even know how to punish the three. It's basically Discord's whispering that leads to the three being petrified. Presumably Celestia herself would not have come up with the idea. Then the villains would have landed again in Tartarus, would have probably escaped, would have threatened Equestria and the ponies again (and probably killed — be it by direct action like half Canterlot blown away or summon an eternal winter). No, in this scene I can actually understand Celestia and Luna. Similar to Discord and King Sombra before, the princesses here use their power to protect their people from an even greater danger. Star Swirl the Bearded would probably have acted the same way. A certain amount of commitment is expected from leaders. No matter what political system. Democracies are also liquidating terrorists.
And you're saying that she could sort of skip all the others with her decisions, but I think you're a little lacking the evidence for this thesis here. You're arguing from your own feelings, which I can understand. But you're exaggerating, I think. Like the Discord thing. Of course, the plot twist with Discord being Grogar was rather weak and might not seem forgivable. But then you also have to take into account that Discord simply corresponds to its chaotic nature. He is the living embodiment of chaos. In this state he EXISTS in this world. He can't help himself. Celestia and the ponies know about that. And they also know that he can
be a friend. Besides, he apologized.
Grin. Of course, this is obviously a weak counter-argument. But it's not! You have to look at it from the logic of this world and the way the ponies think. For us human fans, the behavior of Discord may be damnable even to be despicable. But we don't live in a world of magical monsters and chaotic tricksters like Discord. Neither are we ponies, in whose own nature there is friendship and forgiveness for the mistakes of others. If you regret your mistakes first. Didn't you notice that of all the villains only Tirek and Co. don't regret anything? Never? Not for a single moment!? That's why they were petrified. Not because Celestia acts arbitrarily or stupidly. No, they are simply not reformable. At least not before the next 1000 years. Or would that be moons…? Uch, Equestrian timeline is a mess.
Your claim that Celestia would simply ignore the decisions and rules of others, I consider to be unfounded. Politics is obviously done by others, Celestia is basically passive all the time, which is why you can't read any authority from it. On the other hand, she shows mostly warm-hearted, almost maternal consideration for her subjects: she does not punish Fluttershy for stealing Philomena, nor Twilight for the chaos in Lesson Zero. But not out of arbitrariness, but because of their friendly nature. In return, however, she must constantly trust that others will solve the problems for her. Celestia is trapped in a web of daily (and obviously annoying) obligations, instead of diverting them like an absolutist ruler to others and making a good life for herself. She and her sister are still in a strong teacher/student relationship with Star Swirl and recognize him as the higher authority. From this no position of superiority can be discerned at all. Because she doesn't have it. Because she's a figurehead, a role model but the reins are in the hands of others.
But you have to be ready at all times to accept that she defends her little ponies like a mother. For this, we all know and love Princess Celestia. But I can understand that after more than 1000 moons she doesn't want to work anymore and prefers to retire. Then she can finally let off some steam. ;-)