Your assertion moving an app out of the App Library takes up more space or creates duplicate apps on your phone is wrong. And you can't change the categories in the App Library. Moving an app out of the library to a home page, where you are correct in that you can organize your apps you want, doesn't duplicate the app. Think of the App Library as nothing more than a pointer to the apps on your phone. Just like if you take a photo and move it into a folder in your Photos app, you will note the original remains in your recents folder, but is also in a folder. You don't have two copies of the photo. You still only have one, it's just pointed to a folder so you can find it faster.
I don't use the App Library to organize my apps. I have them in folders I have named as I see fit. You can do the same, without worry that you are duplicating anything or taking up more memory on your iPhone.