It was mostly an argument in favor of democracy and some kind of redistributive system.
Marriage contract? In Rousseau's time many women did not have those either.
It looks like the first welfare programs started in France in the form of limited government funding for charity hospitals in the early 1900's, about 150 years after Rousseau's death
When you break a legal contract, you get sued in court. When you break the social contract, the mob rises up and kills you and everyone like you that they can get their hands on. So the rich and powerful had better treat it like it's a real contract, because it's what protects them. It keeps them in a world where they are the rich and powerful, and keeps them from a world where power is only fists and guns. The rich and powerful don't want that world; they want this one. So they'd better keep their side of the social contract.
We take this for granted today, but it was not always the case. Prior philosophy essentially held that the rulers had a God given right to power, and people had a philosophical duty to obey, no matter how they were treated.
There has been a lot of scope creep since the 1700's increasing the scope of government expectations, and deemphasizing the obligation to take action and revolt if you are not happy with the balance.
The original idea was very real politik, where people are only entitled to what they are willing to risk their lives fighting for.
A state is considered intact if the government has a monopoly on the legitimate use of force. A state can become predatory if they abuse that legitimacy, but other than that, if the government loses its monopoly, you have what is referred to as a failed state.
To nowhere, since there's nowhere else to go.
A) You are born into a system without your permission, and must abide by the rules of those in power or you will be punished.
B) Laws can also be morally sound and in place for good reason.
Except there's no such thing as free immigration right now (except within the EU) and even if there were it would only be a market among offerings and there's no option for non-participation since states dominate all inhabitable territory on Earth.
It's even voluntary in that you can expatriate. But to expatriate you must find another state to immigrate to, and if you don't like any of the social contracts available then tough luck.
“You need to give me free education because of our social contract”
Which really means “give me free stuff cause I want it”.