You want to allow users to take pictures in your app. Which is not an advantage of creating an appropriate intent, instead of requesting the camera permission directly?

Users can select their favorite photo apps to take pictures.
You do not have to make a permission request in your app to take a picture.
You have full control over the user experience. The app that handles the camera intent will respect your design choices.
You do not have to design the UI. The app that handles the camera intent will provide the UI.