Lessened maybe slightly, never eliminated. There will always be an underage market just like with other age restricted products. Even the folks that are old enough to by will try to avoid the taxes much like you see in the States with ridiculous cigarette taxes, buying black market smokes. Also the turf wars between traffickers will likely become more violent as they compete for a shrinking market.
The underage market is there even with the high end black market. And inflating the viable age to 21 for everything artificially inflates the underage market. If you can vote and be drafted to pick up a rifle and fight, you should be able to smoke and drink.
The key to reducing the the low end black market is to be reasonable with taxation, and I believe some of the places where it is legal have seen that and made changes.
There may always be violence, but again, the # of people willing to go guns blazing for $1-$2 a pack is a lot less than the people willing to do it for $10-$20 a gram.