Oh and yes, it would end illegal trade to the extent ending the prohibition of alcohol did.
I live in Finland and black market drugs are 1000x easier to get than black market alcohol. Or black market guns for that matter. Both exist, but not really.
Everyone knows someone who sells drugs of some sort. Most people’s definitely don’t know people who sell alcohol or drugs. Well, alcohol is slightly more common, but usually it’s just flogged tax free or even completely legally ordered in bulk from Germany and then sold to friends.
But yeah, the science is in and yes, legalising drugs would kill the illegal drug trade.