Im in favor of expanding the Child Tax Credit, support a Swiss Style Healthcare System but at the end of the day the family is the best social safety net you can have.
If you had a system say where parents help provide for their kids until they are set in their careers you could reduce a significant amount of debt young people face, and would help them build up their wealth in a critical period as well. Then later on in life when those parents are retired and need help , their kids can help provide for them to ensure they don't need to go to a nursing home(unless they have a critical medical condition), and dont have trouble paying their bills in their old age.
Doing this doesn't even really require people to spend a lot more money, as just allowing their kids and parents to stay in their homes with them which would do a lot . This also then would would reduce aggregate housing demand overall which then would lower housing prices and thus making it easier for families to afford homes which would help the working class as well. Lastly it would also help reduce carbon emissions as well so would help fight climate change as well.
The fact is the Family is the best social safety net someone could have and the destruction of it has caused a significant amount of economic/social problems we face today.
This seems like a recipe for continued economic stratification, reduced social mobility, and making it even harder to get fertility rates back at or above replacement level.
People in the top 10% or so of society will throw any amount of money that is necessary at keeping their kids in the top 10%. Private schools, tutors, bribing college admissions officers, paying for extracurriculars and internships and test prep, paying their rent all through their 20s so they can work in a prestigious but low-paying job in order to position themselves for more competitive jobs at superstar firms.
No one else can afford those things so their kids end up never getting a chance to ride up the escalator unless they are deemed sufficiently "interesting" by the DEI-Industrial Complex.
In my experience, I have never met a separated/blended family (divorced and/or remarried parents) that wasn't dysfunctional to the point where the children viewed moving out at age 18 as a respite from an insanely toxic domestic environment. That's a big obstacle to your suggestion of multigenerational housing. You don't want to live with your mother who you hate or your stepfather who you resent or your half-siblings/step-siblings who you never had a good relationship with.
Part of the reason the only people who make that work are recent immigrants is that they come from cultures where people don't expect their marriage to make them happy all the time and they keep their personal problems to themselves.