While a government-subsidized daycare service is certainly one potential solution, I don't think it necessarily addresses the root causes of these problems.
No. Most changes that will make significant impact on society and social programs have many
root causes that need to be addressed. The most difficult thing about effecting change on a wide scale is getting people to appreciate that everything
impacts everything else
and that the only real solutions must be comprehensive: if you are dealing with homelessness, poverty, single parenthood, then affordable housing is a stopgap; it should show financial returns on top of improving the situation for people currently struggling and help fewer people to find themselves in this situation in the future, but the most ideal way to handle any problem is to prevent that problem in the first place.
On the other hand, it's not acceptable or feasible to ignore the symptoms of the problem either. Repairs to these sorts of problems need to be made comprehensively, dealing simultaneously with the people who are in trouble now (like single mothers without support who are facing felony charges for not having a place to store their children during a job interview) and preventing similar problems from coming up in the future (for example, by improving quality of education, accessibility of resources, changing attitudes toward reproductive freedom, etc.)
In the meantime, however, saying, "Look, subsidized housing for the homeless shows financial gains and loosens the burden on the taxpayer over simply leaving the homeless to fend for themselves which is actually really expensive
for the rest of us," is a better idea than saying, "We need to completely rewire our society from the groundup to fix all of these problems." A comprehensive solution isn't always viable; one step at a time.