Or to put it another way, assuming that I share a common moral sense with my fellow citizens, I would much prefer a legal system that is strongly associated with morality than one that is not.
If your objection is that the law feels to retributive, then that is a separate issue.
To maintain existing power structures
The issue with morality based laws is that morals are subjective. I would prefer a legal system with absolutely no morality - instead being based off of reason and logical conclusions. Being explained well enough in layman terms that people can see why the law is the way it is. "Pay your taxes for schools and roads. Don't kill you neighbor because you wouldn't want to be killed. Don't steal because you wouldn't want to be stolen from."
Morality based laws is how you end up with "It's criminal to be a homosexual. Skirts must pass the knee. Cannabis and alcohol are only for bad people. You must be [religion] to be moral, because only immoral people aren't part of [religion]".
Reason and logical conclusions are not contradictory to a citizenry's moral intuitions, but are orthogonal to them.
Existing laws in the US are largely based on protestant morals. That's kind of the point I was going for: morality based laws can change on a whim once the publicly held views of what is moral changes and that should be seen as a bad thing and it is unfortunate our current laws are so heavily rooted in morality instead of reason. Also, the two can overlap! I'm not saying they never can, I'm saying they sometimes don't. And the times in history where they don't overlap is where you'll see many of the largest crimes against humanity committed simply because it was "legal (and by extension: moral)" to do so.
Perhaps it's meaningful the other way around, too. So many people I see don't want more rigid tax laws, because morals are enough. I argue that morals guiding tax laws only cause to harm those good enough to have morals following the tax laws.
It would seem morals should perhaps guide the desired end result of the law, like no killing your neighbor, but the laws to get to that end state might be counter intuitive. Something Americans suffer greatly from grasping.