"our understandings of liberty and natural rights"
^^^ That depends on who "our" is. There are an awful lot of people these days--the thought crimes, hate speech, etc crowd--who don't seem to have any grasp whatsoever of liberty (liberty for anyone who isn't a clone of themselves anyway). So theoretically a "social contract" is needed just as much now to counteract the far left equivalent of the old time "religious code of ethics." Modern progressivism really is the exact same thing as the past's runaway religious zeal: it aims to force its views on others and control them.
What I find interesting is how people hang onto the "social contract" catchphrase of Beccaria's writings but have dumped all the other elements that I dare say make it most feasible. Laws aren't plainly written, spirit of the law abounds, and activist judges are practically writing their own laws (that they then enforce-or not.) So if Beccaria's supports for a social contract have already been eroded, is there even a good basis for one anymore?
True, I would love to hope that most people are capable of logic. Mostly my argument in this case is to get them to concede that you cannot logically force someone to behave against their will. Every time they contradict that concession I hold their feet to the fire about it.
Common law, like we have in the US is completely borked. We can't both have a codified and clearly written code of laws, and also a system which is created through a compilation of case law and legal precedents. The best way to have a legal system is Civil law tradition of most of Europe (not to say that the current EU legal systems are good, they are just cut from a better cloth).