It can minimize the value of those things for the people that have them... at least within its borders. I'm not convinced that's in anyone's best interests, though.
It can do the second, and it can create opportunities for the third. And it can help (or hinder) the first. (As a purely hypothetical illustration of that, it could implement a systematically racially biased criminal justice system and engage in a pattern of racially-suitable violence against a specific segment of the adult population, decreasing the number of two-parent present families in that segment.)
You're right about it affecting the first, though. Also as a purely hypothetical illustration, it might create a multiple generation-spanning dependency on social programs, make single parent households more economically feasible and socially acceptable as a lifestyle, and foster class warfare that downplays the importance of one's own choices by blaming only others for one's own outcomes.
My opportunity to succeed (which drives my potential income, which drives my potential wealth) is not equal to that of a guy whose parents are billionaires, went to private school and an Ivy League college, and has a contact list full of CEOs and high up politicians. My opportunity to succeed is also not equal to that of a guy whose parents are divorced and poor, lives in a gang-ridden neighborhood, and is stuck in the school-to-prison pipeline. The playing field is not level.