The girl's ambition is pathetic. Does she have some kind of inferiority complex with other people's talent? Without competition, you'll be stale and stop growing. Unlike her, other people don't have previous reincarnations like Avatar. Just pure talent, hard work, or both.
Sounds like it honestly. But it could also be something else; the logic here is essentially "if nobody else exist, i'll be the greatest of anything they can't be" so honestly she would by flawed logic be the pinnacle of not just alchemy but literally everything else. And she will have proven this nonsense to NOBODY because there's no one else around to praise her for it or acknowledge it
I'm assuming she's not actually this stupid, if everybody else ceases to exist she can't be reborn either, effectively stopping the witch's existence and when the current her dies she essentially subverts her own goal by her own logic. When she eventually dies, she won't be the greatest anything anymore either; and just a dead world will be left.
Me thinks that's he real goal tho, stopping the existence of the witch's memories/legacy and stopping the cycle of reincarnation., that would be the only thing that would get done.