Having been a ‘watcher’ of the forum for a while, I’ve decided to take the plunge and sign up!
Would not a picture like the below explain the width of platform that the dancers balance on? (I hope I inserted it correctly!) If the platform where to be any narrower I’m not sure where a dancers toes would go! If you were to use a platform that was wider than the width of all of your toes when on pointe, then surely that would be dangerous for the dancer as there would be a lot more room for movement within the shoe when on pointe/balancing and therefore a lot less support from the shoe. The box of the shoe is designed to encase and support the toes, to keep them straight and aligned when on pointe. This Wikipedia article does explain about the history, development and construction of the pointe shoe: https://en.wikipedia.org/wiki/Pointe_shoe
A properly fitted pointe shoe should match the shape of a dancers foot especially their toes and support the correct alignment of their foot: e.g. if you have long tapered toes, then you can use a narrower box/platform, but if you have shorter even length toes then you would need a wider box/platform. Useful article here on RussianPointe.com: https://www.russianpointe.com/perfect-fit/finding-your-perfect-fit/perfect-pointe-shoe-fit/
I know that most professional dancers have customized shoes, but as I understood it they alter the length of the vamp, how high the shoes comes up on their heel and along the sides of their feet, how long the shank is etc., but I'm not they would alter the width of the platform?