If the Mosaic law was created to get people to sin more rather than less, as Romans chapter 5 tells us it was, then it seems to me that the people who want the 10 Commandments posted in or around court houses and schools are actually encouraging sin rather than discouraging it. Which isn’t the end of the world, I suppose, since where sin abounds, grace much more abounds, but it does seem contrary to the whole point of the Christian religion (not that its followers are known for their consistency).
The 10 Commandments are only 1.63% of the whole Mosaic law, by the way (and yes, the 10 Commandments are a part of the Mosaic law, as Paul made clear by referencing the 10th commandment when he wrote Romans 7:7–9 as a part of his teaching that we shouldn’t allow ourselves to be placed under any parts of the law at all), and if you choose to obey one part of the law you’re then obligated to obey the whole thing, or so Galatians chapter 5 teaches.
Since those of us under grace no longer need the law, I’m quite happy to leave it behind the way I did my school teachers when I graduated. It served its purpose at one time, but to try to keep the 613 Mosaic rules now would be just as silly as following the rules of the classroom now that I’m no longer in school. I’m past the need to raise my hand when I want to speak, and I’m past the need to avoid bacon when I want to please God. Sure, some things just make sense to avoid, such as killing people or pushing people on the playground, but that’s because they’re not nice things to do (and might land you in prison), not because God is going to get you for doing so.