The concept isn't hard to get your head around. Businesses draw up similar contracts all the time. You're just expressing a formal mutual accountability. It enables one partner to "safely" make sacrifices (or exploit time preference).
If you don't want to be accountable to each other in a formal way, by all means, keep your relationship informal.
Marriage has privledges it grants that you may find necessary when you least expect. Medical responsibility is one of them. You don't have a say in their medical treatment if they are unconscious or otherwise unable to make judgements.
I understand not wanting the religious part, and I understand reviewing the cons of marriage and rejecting it, but making it about the 'government knowing' is the least of the problem really.
In the case of divorce that actually becomes very important. You now have a judge from the government who is making life decisions for you and your family. Source: grew up in a divorced household.