Modern Browser complain if there are non-https elements in https websites. This makes sure that if the user visits via https all elements of the page are also retrieved using SSL. Furthermore it uses https urls in emails that are send to the user, if SECURE_URL_BASE is set in project/project.inc.
The only remaining places where URL_BASE is used is when it is used as master_url where it is important that it is in sync with what the scheduler uses.