A liberal would tell their “client”, “There’s food stamps, utilities assistance, housing assistance, check-ups, vaccinations and drugs at the health department”. The client would say “Thank-you”.
A conservative would say, “They’re hiring over at such and such. Schooling is available to get a skill or education to advance to a job with better pay and you could in a couple of years rent a house and move out of the project”
The client would say: “But then I’d have to pay my own bills for food, rent, utilities”. No thank you.
In addition to your useful discussion of the “social welfare” part of “social work,” many people with degrees in social work are in the counseling profession. Theodore Dalrymple wrote at length about the difficulty of genuinely helping people when you’re not allowed by the professional rules to address the “client’s” personal choices.