> The war on drugs is not a war that soldiers fight
Debatable. The police men / DEA involved probably feel like soldiers sometimes. The drug lords and governments in south america certainly have soldiers involved.
They're being trained to think of themselves as soldiers. This will inevitably lead to them being soldiers, and that eventually ends in bog-standard straightforward war, indistinguishable from any waged by "real" soldiers.
Most soldiers throughout history were not career soldiers or warriors. Most are people brought into the conflict without any intent to be a soldier before whatever brought them in.