In a system where there are no tax-collectors, there may be no one (state mechanism) you can expect ("let others do it") functions from. Therefore, the financing should rather be built-in, as an integral part of the process of satisfying those human needs.
Here, it is.
In other words, my system is seamlessly self-financing. The concept of "state money" is non-existent here. Hence, no taxes - as the state money when being collected, is called.
Islamically, each year, a zekat-giving-able person must give some percentage of his/her money to the needy. Ratios differ, but for cash and such, it is 1/40 (2.5%) of not-personal-use belongings, each year. See some fiqih text to find out ratios, and for the zekat giver vs. taker breakpoint. One who is below that point is eligible to receive. (Being poor is not the only category of neediness. Some others, needy-at-context, may receive zekat. See fiqih books.)
Observed strengths/features of zekat include:
It is a compulsory function for the giver. Yet, it is really not such an important amount for the giver.
With high-probability, the given money will re-enter market soon because, by definition, the recipients are among the most needy. They would use the money.
That amount of money will pass to some among the most needy. For them, it may be important. (Consider social unrest, etc., too. Especially fine because zekat is compulsory. It is being supported, without being indebted to anyone, either materially, or with soul. Of course, good feelings may be. But that is actually what may happen when it is not required.)
Not so likely to get rid of the motivation to work because one cannot count on his/her being among the upcoming zekat recipients from someone. No guarantees. Zekat giving is compulsory indeed. But, to-whom it will be given is a matter of judgment.
Among the zekat-receivables, the giver or the distributors (if any such, there), may decide whom to give. That does not mean the choice may be arbitrary, especially given that Allah is demanding good conduct in this, and the zekat-giver cannot act as if doing some "extra" "favor" to that who he/she is giving zekat. It is an obligation. And should be executed in best judgment, as well as in good manners.
As an issue of extra favor, Islam also promotes sadaqa/infaq (giving to the needy, etc.). Not compulsory but makes positive points for other-worldly status, and receives favor of Allah. Lending money without any interest is also promoted (indeed, even more than sadaqa at a base comparison, because the debtor is mre probably in need). Further, in Islamic countries, waqf (foundations) have in past centuries (and still) been helpful to others.
These all are part of the bottom-line. Coupled with the system of incremental gains I describe at this site, this is probably optimal, as far as it goes.
And in case you wonder what is the last point at the bottom-line: Nobody should die out of hunger. Or, in more precise terms, when somebody may die if he/she does not eat, what otherwise would be called theft of some food, becomes a right. As a result, the society, where this system is in application, should rather ensure that much - which is almost always close to being guaranteed anyway (zekat, sadaqa/infaq, and those foundations have kept being sufficient.)