An excellent post! The only qualification I would add is that means-tested govt. social programs have been also run as if they were private charities, even before the 'welfare reform.'
As far as I know, never in the history of US welfare programs has everyone who is legally entitled to assistance received it, and not simply because of technical mistakes on the part of social workers. In fact, the gap (between entitlement and actual delivery of assistance/service) grew bigger in the era of working-class acquiescence, and it became narrower when social movements were on their upsurge. I wish folks had publicized this fact more when we still had a slim chance to save AFDC: welfare programs have always been severely underused.
Yoshie