My mother absolutely refused to leave. I had to go down there and drag her out. And this was 5 days after the storm hit.
Even after I got to her and explained that she had to leave, that she could not stay, that there would be no power, water, or food, she still insisted on staying. I finally told her that I was taking her out if I had to tie her up (not, I assure you, an idle threat) so she could either pack a bag and take something with her or she could travel as is.
There are, I am sure, a great many people who stayed because they had no way of leaving, but this is not, in my experience and estimation, the case with anywhere close to all (or even the overwhelming majority) of the people that stayed. Of the people with whom I had contact during my trip to get my mom, none stayed out of necessity; all stayed by choice. And few of these people had any idea that their very presence, even absent any pressing personal danger, increased the burden on the rescue and recovery effort.
What happened in Orleans Parish is hardly a surprise; it has long been understood that there existed no plan in place to provide for people who ignored evacuation orders. The implication that the Superdome was intended as some sort of "rescue center" is dead wrong - it has always been intended as a shelter-of-last-resort to protect people from the wind, collapsing buildings, and flying debris, only to be used if you could not get out of town, and only during the storm itself. It was a classic BYOB party - bring what you need and sit out the storm. It was never intended as a primary evacuation center or long-term refuge facility.
Lest anyone misunderstand, I love New Orleans. I lived there for 11 years and my parents moved to the area in 1978 and never left. But the reality is that while it calls itself "The City that Care Forgot", it is as accurate to call it "the city that forgot care". The city is culturally and politically incapable of planning for unpleasant events.
I am not surprised that transportation was available but not used to evacuate people - that is the nature of this particular beast.