When the gov't attempted to prohibit drug use, it created the opportunity for a black market in prohibited drugs to thrive. If you can accept the following:

  * Some people are going to take drugs without regard to legality.
  * Some people are going to fill the market's need for drugs through smuggling or manufacturing.
  * The government is utterly incapable (by design, actually) of completely preventing the above.
  * Without criminalization of drugs manufacturing and sales, there would be very little or no reason for violence in the drugs trade.

Then it's fair to say that criminalizing drugs use is the cause of the violence, or at least that decriminalizing drugs use will result in a reduction in violence.

>violent street gangs long predate any restrictions on drugs or alcohol

Violent street gangs opportunistically traffic in contraband because prohibition creates a dearth of supply, driving prices high enough to support an illegal black market.