Will chariable healthcare giving to the poor materialize?

Comment to Arnold Kling's EconLog post on health care, where Kling makes a statement about health care charities materializing if the government stopped supplying health care.

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> If you took away government, then my guess is that a lot of charity would go toward health care for people with low incomes...

I am not so sure.  That would depend on a large number of Americans acting with economic irrationally, and I am not aware of the evidence of such Americans existing.

Lets peg current monetary charitable giving in America, from all sources, at $350 billion.  Lets consider the 30 million Americans living under the poverty line.  Lets spend on each $1500, less than half of the $3600 that Canada spends on each citizen, on average.  So we are counting on over 12% more charitable giving to take place, to fund this calculated $45 billion.  We will assume that much more than this is relieved from the tax burden, so tax payers have more money in their pockets, to spend as they wish.

No matter what a person thinks of the poor receiving health care, a single person's contribution would have no measurable effect.  Whether an individual gives or not, the poor will still have the same access to health care.  So it is irrational for an individual to give charity.

You would have to rely on a group of people that have, as a compelling component of their identity, the need to contribute to the welfare of the poor.  We hope for something substantive, not at all like Mother Teresa's charity in Calcutta.  Mother Teresa's charity in Calcutta, while being a sincere expression of great sacrifice, made no statically significant improvement to the lives of the poor there, because, measurably, only palliative measures were given out to a statistically tiny number of poor.  Nothing like a functional health care system for Calcutta's poor came out from it.  We need tens of billions given, with regularity so building projects and professional salaries can be funded, to realistically call it a medical health care system.

Is there any evidence of a large enough number of Americans, large enough to fund a poverty health care system, that have the irrational compulsion to give to charity, because they have as a compelling component of their identity the need to contribute to the welfare of the poor?  I am not aware of any evidence.  I don't even see evidence of $100 million in charitable giving for American health care for the poor.  At at least $500 million, it would be significant enough to break out as a health care funding source, and there is no evidence that anything approaching that exists.  I doubt the poor state of current government health care programs would be enough to totally squelch their concern for the poor receiving adequate health care, if that concern really existed.  So, where are the hundreds of millions, already being giving now?  (We are talking about a reduced level of giving because funds are already coerced away by the government).

However I feel, morally, about the poor having access to health care, I don't place any faith in economically irrational behavior, here.  The human causes of economically irrational behavior are finite, when we limit ourselves to causes that are sufficient to surrender tens of billions of dollars from wallets, with the quarterly regularity to fund systems that include buildings and medical supplies and medical technology and thousands of professionals.  Such economically irrational behaviors have present day and historical consequences we can see.  They seem, to me, to be very well hidden, if in fact they exist.