Parishes exist to serve the people within its boundaries, not for lay Catholics to feel beholden to it like serfs. In other words, you have a canonical right to receive the sacraments at your geographic parish (the one whose lines on a map your residence falls within), but you don't have to be exclusive. You may fulfill your Mass obligation at any Catholic church, including Eastern rites.
Parish registration may, however, be necessary if you wish to receive sacraments like baptism, confirmation, or marriage, as you say. Also, if you regularly attend a parish that's worth supporting, I certainly do recommend registering and going all the way: supporting it with monetary pledges, volunteering on councils, altar serving, and so on. Just because one legally can treat a parish like a sacrament factory doesn't necessarily mean one should.