alt Hacker NewsWell off people do not allocate capital in a way that's socially or economically (on a national level) optimal. So the government has to do that for them (even if those who the majority of taxes personally benefit less from that than if they were allowed to keep that money).
I don't think that's entirely unreasonable. After all there are hardly any personal incentives for individuals to invest into infrastructure, education or healthcare of people who can't afford it and plenty of other areas even if that's what allowed them to accumulate a significant proportion of not the overwhelming majority of their wealth over the long term.
If there's hardly any individual desire, as you say, to fund the development of the poor then taxes in that pursuit are illegitimate under a theory taxation happens by the assent of the people (even if only roughly a majority or their representatives).
Given that most taxation done with the the advertised goal of helping the poor in Australia does happen with popular assent of individuals, I would theorize your position is false and that people do have some individual incentives to develop services offered to the poor -- for profit, humanitarian / charitable reasons, and a variety of other considerations.