It's a simple matter of public health.
http://en.wikipedia.org/wiki/SyphilisYou can always live together as "common law" if you do not wish to be granted benefits of state by simply complying with the rules of state.
Syphilis is not spread through exchanging vows or signing documents at the court house. To my reasoning, you'd be much more likely to catch syphilis from someone you weren't planning on marrying. I just don't see how the state having these rules is going to prevent the spread of syphilis, when it has no influence over how syphilis is spread.
This may be a holdover from a time where when a woman got pregnant, the man would marry her...I think (if I recall correctly) that the issue with syphilis was not necessarily to protect the adults, but to protect a fetus from conginital syphilis....definitely from a long time ago, in a galaxy far away...
(That last part was for McFranklin)