No, disaster relief should not be removed from the duties of the American Red Cross in favor of more competent outfits, because the American Red Cross does an excellent job of disaster relief. If I were the victim of a disaster, I would much rather have the American Red Cross show up at my door than FEMA.
In times of disaster people recognize American Red Cross as a helping entity. In times of disaster there can be a lot of chaos, but people know help is near when they see the red cross symbol . It is a brand that people know. The American Red Cross has shown to be a competent resource in disaster relief efforts.
It would make little sense for the Red Cross to be completely eliminated from the equation of disaster relief assistance. Although there are imperfections in the system, it is wrong to completely eliminate the aid assistance because a few hiccups or problems exist. Their hearts and actions are in the right place, and if anything they should work in conjunction with other people.
The Red Cross is there to help and aid people who have been injured and have damaged lives from disasters. They are the biggest contributor outside of government's random money grants that actually help the people as victims. They should not stop aiding disaster relief because it is essential to this planet.
I have not seen more competent outfits than the red cross, so to me, this is not possible. If an outfit comes out that is more competent than the American Red Cross, of course I think they should assume the responsibility of diaster relief and that the ARC should be outsted.