Make optimistic assumptions about the economic results of privatizing everything, and need may greatly be reduced. Make pessimistic assumptions, and mutual aid remains, strengthened by the absence of government interference and crowding out.
The things that people, especially progressives, like about the government "taking care" of the poor:
* the government can force those other bad people to pay their "fair share" whether they like it or not.
* someone else's problem, I don't have to get my hands dirty but I don't have to feel guilty about it either.
* if people get to choose whether or not to contribute, there may not be enough money. Under the current system, if there's not enough money, I can blame those bad people who disagree with me politically.
How much money is wasted by political lobbying on each side of this issue? How much of this effort consists of the cheerleaders for each side goading their supporters into a group frenzy of team spirit, aimed more at perpetuating the process than accomplishing the goal?
I suspect that if this was done by rational people with serious goals, they would build in metrics to measure how successful government programs are and how cost-effective. They would encourage different experiments to gather knowledge and experience, allowing participants to give input into how they are helped and what they consider success. My (admittedly biased and non-expert) opinion is that the system is bureaucratic, monolithic, insensitive, and unaccountable.