Yes, the evacuation was mandatory, but there wasn't enough time to actually enforce it. If officials came across people who refused to evacuate, they had to choose between taking the time to force someone out vs going to the next home and helping someone who didn't have the means to evacuate.
New Orleans is a very Poor city. My friend's niece is a school teacher there and she get about $40 for classroom expense per YEAR. She has to spend a lot of her own money for supplies.
Also, there is probably even less street parking in NO than there is in NYC. Not everyone owns a car because of the expense.
The 2nd problem was that there was no where to go. The roads were jammed. Even if one got on the road, you probably weren't moving. Eventually, it would become a choice between being inside vs stuck in a car. Being inside is the safer choice since cars can easily be swept away and are more vulnerable to debris. Before the evacuation was ordered, news reports cited that there were no more rental cars available.
The hurricane itself was survivable. The villian is the water and the breached levees. If the levees hadn't been breached NO would not be under this much water.
I saw the governor of Louisiana on CNN. She said that the airlines could have stayed open longer, which would have allowed more tourists and others to leave and lightened the load on the roads. According to her, there were very few planes leaving NO on Sunday and the weather was clear enough for planes to fly at that time, but the airlines cancelled the flights, instead.
Obviously, the area needs a better emergency plan. The problem with these types of plans is that they aren't always reviewed and updated for growing populations, etc.