I think, you haven't got the Moodle way of thinking. On a Moodle site _registration_ and _enrollment_ are two different things. Registration is a site-wide thing, need to be done only once, username and password belong here. Enrollment is entry to courses, you mentioned two, there could be more. Having registered on the site doesn't guarentee the entry to courses, it is an additional step. Knowing the username and password alone are not enough. In the jargon people talk of authentication vs authorization.
P.S. If you manage a Moodle site, you might want to take a Moodle administration course in the
Moodle Academy.