There is a ton of research on various questions related to this, and I'm not familiar with it in any detail. I'll just point you to a few examples of meta-studies, which each review the results of many other studies.
"Does drug education work?" (2000)
Recent research indicates that certain drug education programmes do stop or delay the onset of drug use under optimum conditions. Social inoculation programmes have generally enjoyed the greatest degree of success, but the behaviour changes have been confined to a small number of students; have not been uniform across all drugs and have diminished over time. Research on the cost effectiveness of drug education progammes indicates that they compare favourably with the cost effectiveness of most law enforcement approaches, but are not as cost effective as treatment. While there are some methodological qualifications, the drug education literature does indicate that soundly conceptualized and rigorously implemented programmes can influence drug using behaviour and that comprehensive provision of such programmes is likely to produce a net social cost saving to society. This does not mean that proven drug education programs will necessarily be implemented. The most powerful factor in the implementation process is selection of programmes on the basis of ideal outcomes, rather than on the evidence of what can realistically be achieved. Ultimately, this is self‐defeating, because programme failures will again discredit the whole drug education approach. Drug education programmes must be selected because they have demonstrated the ability to have a beneficial impact on youth drug use and youth drug problems.
"Drug Law Enforcement: A Review of the Evaluation Literature" (2007):
This article describes the results of a systematic review of drug law enforcement evaluations. The authors describe the search procedures and document the results in five main categories: international/national interventions (e.g., interdiction and drug seizure), reactive/directed interventions (e.g., crackdowns, raids, buy-busts, saturation patrol, etc.), proactive/partnership interventions (e.g., third-party policing, problem-oriented policing, community policing, drug nuisance abatement, etc.), individualized interventions (e.g., arrest referral and diversion), or interventions that used a combination of reactive/directed and proactive/partnership strategies. Results indicate that proactive interventions involving partnerships between the police and third parties and/or community entities appear to be more effective at reducing both drug and nondrug problems in drug problem places than are reactive/directed approaches. But the general quality of research in drug law enforcement is poor, the range of interventions that have been evaluated is limited, and more high-quality research is needed across a greater variety of drug interventions.
"Effect of drug law enforcement on drug market violence: A systematic review" (2011)
Violence is amongst the primary concerns of communities around the world and research has demonstrated links between violence and the illicit drug trade, particularly in urban settings. Given the growing emphasis on evidence-based policy-making, and the ongoing severe drug market violence in Mexico and other settings, we conducted a systematic review to examine the impacts of drug law enforcement on drug market violence. [...] Our findings suggest that increasing drug law enforcement is unlikely to reduce drug market violence. Instead, the existing evidence base suggests that gun violence and high homicide rates may be an inevitable consequence of drug prohibition and that disrupting drug markets can paradoxically increase violence. In this context, and since drug prohibition has not meaningfully reduced drug supply, alternative regulatory models will be required if drug supply and drug market violence are to be meaningfully reduced.
So to summarize I would say that you are probably correct that reducing demand is more effective then trying to crack down on supply, but the two may be complimentary when they include community engagement. Education can help, but addiction treatment is especially important.
