All good in theory but for that to happen, invest needs to be made in healthcare, staff, funding for charities, funding HMRC and Child support agencies etc etc. Not cheap, so how would you pay for these investments.
There's that saying "buy cheap, pay twice". That's kind of what the false economy approach is.
It also won't be as costly as people might think. Massive amounts of money is spent on housing and public services. It's just misspent - and then costs society and taxpayers more.
Housing for example. Billions is spent just on temporary accommodation. Add in the many millions (probably billions) on housing benefits for private rentals, and it's cheaper to fund more council housing.
More social rentals would also reduce demand for and cost of health and social care. Private renting is more harmful for health than smoking. I assume short-term when young and maybe not yet settled in an area, it's fine, but doing it long-term and/or when older, vulnerable, or a family, is when it affects health.
Then there's public services - health and social care, DV services, mental health services, etc. Outsourced to private companies or charities who pay senior staff and owners eye watering sums and prioritise spending on PR campaigns and bidding for contracts.
Because of their spending priorities, they often have badly trained and low paid junior frontline staff (who often need benefits top-up). And the services provided are done on the cheap and substandard.
So this costs more money - because the people needing support end up in more need of help and for longer periods of time, and the frontline staff need benefits to top-up their wages plus often suffer burnout and end up in need of support services or sickness benefits themselves.