Your post is ideological - sweeping application of game-theory style logic, but without the evidence to suggest that the logic applies to this case.
1) 'Governments are similarly inept at spending their money efficiently' is overly simplified. The most obvious counter-example is that the US and the UK spend the same amount of tax money as a percentage of GDP on healthcare; the former gets limited programs covering a minority of the population, the latter gets a universal health service (albeit obviously with limitations).
2) On what basis do you say that no large scale NGO disaster responses work out well? I would say that is an incredibly difficult conclusion to draw.