Secondly, there might be some advantages to having ordinary people living in New Orleans. (The level of damage varies a lot depending on the neighborhood. Afaik, the planned evacuation orders also vary by neighborhood.) They can at least do some guarding of their houses and start to rebuild.
It's going to cost something to supply them with food and water, but it's going to cost something take care of them elsewhere, and the resources elsewhere are stretched pretty thin, too.
People's pride and determination isn't some dispensable little thing.
The people who are staying have more detailed knowledge of their situation than the people who want to force them out do.
Having people in New Orleans increases the pressure to get basic services and the clean up done quickly. See above about the benefit of the doubt.
The argument in favor of mandatory evacuation is the risk of disease, and I grant that it's a serious argument and it may come from the geek side of government, the part which has been ignored to such disasterous effect.