That’s part of the reason I like the original story more—the beast was a good dude from the beginning so when Beauty (she wasn’t named Belle. A lot of these stories don’t give names to their characters) comes to love him, it’s basically the message that no matter what he looks like, if he’s a good man, he can still be a prince in your eyes. This impact is arguably lessened in the Disney version by making him cruel to her in the beginning, so it’s kind of combined/tied up with the Beast becoming worthy of her love by being changed by her for the better, and when that moment happens, he becomes the prince. He’s good on the inside now, so he becomes good on the outside. Of course now you’ve also got people diagnosing Belle with Stockholm’s and stuff like that.
I like the slightly greater subtlety in the original, where the Beast changes physically, but metaphorically it’s Beauty that changes.
The Disney version was also very heavily influenced by feminism at the time, hence Belle’s differentiation from characters like the Bimbettes and why Gaston acts the way he does. Gaston is a Disney creation—the closest things to villains in the original are Beauty’s shitty jealous sisters. That being said, for a film, Gaston and the Beast having a showdown makes for a better climax than the original which just has Beauty’s shitty sisters’ machinations causing the Beast to die from loneliness which is laughably mundane in comparison, so that’s something I’d want to see reworked a bit if there was ever a more faithful adaptation.