Hello, I guess another approach is to add this new Page Type into one website and then export it as a pag type package and then import it, when you create the new website.
Now if you want this page type to be in the tree and also something that needs to be used for every new website, another approach is to create this page type on a blank website and add the relevant security settings for the page in the tree. Then use this as a website template for all new websites and you will have the page type with it's setting in place each time.