Why is prohibition often referred to as the “noble experiment“?

The phrase "noble experiment" really reflects on the difference between what law does and what was the intention of the law. Herbert Hoover knew that the law was far reaching and said phohibition is, “a great social and economic experiment, noble in motive and far-reaching in purpose.” Law is concrete, but the affects are social and can have unintended consequences.
The phrase captures the modern notion of changing social norms is not simply making a law, but drafting policy and often using extra legal measures to alter the intended harmful norm. The prohibition is referred to as the "noble experiment" because is is a prime example that a law may have undesirable effects despite how good the intentions may be.
The prohibition was meant to alleviate the ills of alcohol. Many thought that making alcohol illegal would eradicate the slum all together. Many thought that without alcohol there would be less drunks, less people in jail and a cleaner society. The truth was that prohibition made matters worse.
Prohibition was a massive failure sparking new crime, gangs, and various illegal drinking locations. Crime rate went up and alcohol related deaths were on the rise due to poorly manufactured and homemade alcohol.Alcohol was mainly smuggled in and smuggling was a large source of illegal activity that resulted in many arrests and deadly altercations between cops and smugglers and also between rival gangs.
Despite the good intentions, the law was grandiose and reached to far and feel to hard and swift. The "noble experiment" wanted to help people from the ills of alcohol, but with rarity often comes high demand. Simply economics were ignored and the law did not take into account that law is much more than telling people to not do something, but law involves politics, social norms, economics, and psychology. Good intentions can lead to terrible results.

President Hoover described Prohibition as “. . . a great social and economic experiment, noble in motive and far-reaching in purpose.” Thus, during this era, Prohibition became known as the "noble experiment." Prohibition was considered both noble and an experiment because the outlawing of alcohol was a completely novel concept that had the potential to radically transform a society, and it was considered a particularly noble experiment because it was an attempt to respond to the immoral and abusive acts that often transpired from alcohol intoxication. Prohibitionists considered their work to be based on morality and often on religion. They saw a strong connection between the evils of society and alcohol consumption, and they rooted their cause in a moral crusade against liquor. Prohibition is also referred to an as experiment because it failed to stop the consumption of alcohol.
http://classprojects.cornellcollege.edu/stewart/Hoover2/Hoover.htm