Not sure if we have the data for this sort of analysis, but I could easily imagine the argument that the economic and social loss caused by the denial of benefits to people who test positive might far surpass the economic and societal loss caused by allowing those people to obtain benefits. Like, maybe I am in the minority here, but I don't believe that looking for any reason to starve poor, uneducated people of their survival resources should really be an underlying tenet of our welfare philosophy.
Additionally, IMO, drug screening is a poor standard of evidence and would probably be a considerably imprecise mechanism both for effectively steering the flow of public money and for encouraging job skills. Testing positive for drugs doesn't mean that you purchased them yourself, so using a positive drug screen result as strong evidence that you would misuse public aid funds screams "Type I error." Positive drug screens also provide zero discernible evidence that you did or would do drugs in any way that was/would be irresponsible for your employment or financial situation. If you believe that it's possible to do drugs (like you know, legally drink alcohol) after working hours or on the weekends without ruining your economic productivity, then I don't see why responsible use should be inscrutably lumped together with "disabling" or "demotivating" use. While heavy use of certain drugs can surely exert their own independent effect on somebody's motivation to live independently and support themselves, a great deal of any correlation between drug use and motivation is probably endogenous. Lack of motivation probably exerts a much more consequential causal impact on drug use than drug use exerts on demotivation. Highly motivated drug users (I'm sure there are few of you in here, hiya friends) can agree. What matters more is probably whether the person is internally motivated and already has the tools to succeed, so treating drug use as some exogenous cause of demotivation would be a humongous analytical flaw, and I think it's generally a bad move to seriously base public policy decisions on humongous analytical flaws???