Are we assuming that the UN humanitarian work would not be done if the UN wasn't around?
Why would we assume that?
People seemed to be defending the UN based on things like disease prevention, etc. I must admit that I suspect that were those resources instead given to, say, Doctors Without Borders or some other less politicized organization we might get even better results.
Any organization used and funded by hundreds of governments united towards tackling a goal will inevitably become fairly politicized. Any organization only funded by like-minded governments (read Europe + the wealthy anglo countries + a few others) will inevitably accomplish less and still be very politicized and be viewed through a negative lense by other nations as a "colonial" organization.