Carrionites are just witches by another name, and witchcraft, magic, is merely a different sort of science. Human science utilises numbers where the Carrionites are all about words.
They hold more power than you’d think.
The right words in the right order, spoken in the right place at the right time, can do anything, even cause the world to end. That’s not something the Doctor is keen on seeing happen. He rather likes the earth and its people.
Earth needs a champion; to fight words, you just need better words, so who better than Shakespeare?
All’s well that ends well.