Please read the article! He gives them the choice between the "standard" punishment (days in jail and such) and his "unorthodox punishments". And the later are, as close as possible, focused on repairing the problem, not punishing.
On one hand, making a nanny who hit a child research and write a report on the effects of child abuse seems like an extremely good way to deter recidivism, and make an impression on the defendant.
On the other hand, making someone do an embarrassing public stunt seems like it would make them famous for the wrong reasons, severely handicapping their ability to find work in the future, to the point that it's ultimately worse than a short jail sentence. Embarrassing someone doesn't fix anything for them.
At least in the examples in Wikipedia, the punishments seem to focus more on making the defendant feel bad (in a hopefully educational way, not merely suffering), which is less good than making some form of reparation or restoration. The legal system already has a notion of community service as an alternative to jail; there is a lot of room for community service that uplifts victims while educating perpetrators.
For example, a nanny who hit a child could be sentenced to XX hours of sewing blankets for children in hospitals and orphanages.
Having the freedom to issue unusual punishments can be beneficial when the judge is positively motivated, but the same powers in the hands of a cruel or vindictive judge offer enormous potential for abuse.
For example, give judges the power to issue unusual sentences, or ones violating the minimums, but have those sentences trigger an automatic review by an independent panel (perhaps a couple of appeals judges or something).
The unusual punisments can be beneficial when the judge and also the defendant, and victims (or their representatives) agree agree that the punishment is restorative.
From the list, it seems that many belong to the "an eye for an eye" category rather than to the "repairing a problem" category.