is it a ligitimate explanation as to why crime is such a problem?

The drug laws are a partial explanation as to why crime is such a problem. Crime rose during Prohibition and it has done the same during the modern "war on drugs". People are no longer killing others in the street over alcohol selling territory, because it is taxed and regulated which keeps criminals out. Alcoholics don't have to rob people to support their habit. If they go broke they can still steal it to support their habit.

The lessons learned from Prohibition were used to create a far more shrewd policy when it came time to ban psychoactive botanicals. This is the primary reason the Interstate Commerce Clause was used instead of passing a new constitutional amendment.