Courts
Shame is an undervalued quality. Only humans have shame, as they alone recognize when their actions have fallen short. A person who acts immorally without shame has lost the most precious of human qualities: conscience. People who routinely espouse a philosophy of "no regrets" are simply attempting to suppress their humanity and liberate themselves from morality, guilt and consequences.
Good luck with that.
Nonetheless, shame was once a central element of punishment. From schoolboys wearing dunce caps to throwing someone in the stocks and the literary scarlet letter, punishments have long relied upon public humiliation as a means of personal rehabilitation and general deterrence - and often as a bit of good old fashion vengeance.
The state has generally lost the power to employ humiliation as a sentencing device - cruel and unusual, apparently. So it's interesting to read that private citizens have offered precisely this punishment as an alternative to prosecution. There is currently an 18 year-old would-be-shoplifter dressed as a Sesame Street character carrying a sign that reads, "I got caught shoplifting at Halloween Express." I'm rather comfortable with people offering private substitutions to would-be criminals - they can always choose the courts, but have the option to give the victim and others concerned with the crime a first say in restitution.
On the other hand, a guy in Houston was sentenced to spend every weekend for the next six years pacing a busy highway with a sign reading, "I am a thief. I stole $250,000 from the Harris County crime victim's fund. Daniel Mireles." His wife is currently serving a sentence for theft, as well - their home has a court mandate sign in the front yard reading, "The occupants of this residence are convicted thieves. They stole $250,000 from the Harris County Crime Victim's fund. Signed, Judge Kevin Fine."
Maybe there's hope yet for humiliation.
Ok, I'll quibble...
But I'll say beforehand that I think your overall line of thought is spot-on... shame and humiliation are powerful forces, and their anticipation works to keep us from engaging in behaviors unacceptable to our personal community. Perhaps only the threat of shunning is a more powerful motivator along these lines.
Now the quibbles... First, even dogs can show shame, and there are times that I've wished that some humans could express the simple remorse for "bad behavior" that I've seen in dogs. I'd guess that shame is actually pretty common in many of the primates.
Second, the term regrets has become so meaningless these days that it is nearly a throwaway phrase. How on earth can one possibly regret what somebody else has done? What meaning is there in regret when it has become a pro forma phrase to publicly acknowledge one's own bad behavior, while not accepting that real consequences are called for.
However, what I personally feel that regret should mean is a personal and lasting shame about those actions (or inactions, for that matter) that I, personally, wish I was not responsible for, and from which I learned no valuable lesson in how to improve my conduct. Suffice it to say that I have no regrets, but there are many sins that I hope and plan to never repeat.
I think we need to bring back the chain gang, or at least some version of hard labor. Five or ten years of that will take the "mean" out of most people, and if we are clever they might actually do some social good through all their labor.