Because the Beast changed for the better and learned to love another and earned love in return. He was a different person from the spoiled prince from the beginning, he had earned her respect and his freedom.
That is well said, Solid Sun...I couldn't have said that better myself.
More importantly why did the Enchantress have more appearances than she did in the animated version?
The filmmakers wanted to expand her role beyond just cursing the prince and then disappearing from the story.
Does Into the Woods ring any bells?
Well...just like the witch, Agathe's role was to make sure the spell could be broken, as long as certain conditions were reached. But unlike the Witch, Agathe showed compassion and saw how much Belle truly loved the Beast...
Sure she cheated, but it was the good type of cheating.