I have many problems with this notion stemming from a variety of rationale, but to get right down to the biggest issue, it is not fair to assume that drug use is always a cognitive choice.
Yes, it's frustrating to imagine drug addicts collecting welfare and using those funds to continue their drug use, but that frustration should not be directed solely towards the user. Perhaps if you're imagining an out of control-hedonistic suburban kid who is exploiting the system, you would have a valid point, but in reality, drug addicts are spawned from systematic problems in society. Why would the answer be to punish them by effectively revoking their welfare and cause them to potentially spiral even more into their addiction?
Drug testing is not at all cheap. The funds that would be used to implement such a policy would be a tragic waste knowing that those same funds could be focused on drug addiction treatment or prevention. Let's use that cash to SAVE drug users, not to use it to ruin more lives just because we don't believe it's fair. Many drug addicts probably don't think it's fair that they got dealt the worst cards in the deck to begin with.
AND this is all under the assumption that drug addicts are siphoning welfare money for more drugs. If a young single mother, who legitimately tries hard to care for herself and others, happened to toke up once last month as, perhaps the only not-poopie part of her life, now we're going cancel her welfare? Are we going to cheer as she and her kid end up in the street because justice prevailed?
You want to talk total welform reform, let's talk welfare reform, but mandatory drug testing for welfare recipients is a inanely simple, harmful, ineffective, and myopic solution to a much more complex problem.