Oh, so many reasons, and it's rather easy to sit in judgment when you are in a position to have choices.
On the issue of homeowner's insurance, don't bet on it. Poor people and landlords usually don't buy more insurance than the mortgage company requires, and most of the time, flood damage is excluded from those policies if you live in a low-lying area. Flood insurance costs extra, that is, *if* you can find a policy to buy, which in some areas is darned-near impossible because companies have withdrawn from the market. Also, the idea that looters will only take items that are valuable enough to be well-insured is laughable -- they will take anything, even things that are nailed down, including ripping out light fixtures and going at the walls with axes to remove copper pipes.
Mentally-ill people usually simply can't take shelters; they are almost always terrified of them. Shelters are full of strangers that may or may not be dangerous, and usually there is no real security in place to make sure bad actors are caught.
Nothing like running to a shelter with every item of value that you possess in the world, only to have someone steal it all the minute you fall asleep.
Most of all, it is the fear of losing everything that they feel makes life worth living. People are scared that if they lose everything they have they will never recover, and if that happens they tend to think that death is a viable alternative, at least until it is actually staring them in the eyes. For the vast majority of people in evacuation zones, the odds of surviving a big storm are fairly good if they have been careful and are properly prepared, and most people who have never experienced a direct hit will be convinced that they fall into that category.
At the same time that forecasting has gotten so much better at predicting storm paths and flooding, home construction has gotten worse at building to withstand storms and flooding. Part of the problem is the advent of air-conditioning. In the days before A/C, people in coastal areas built homes up off the ground with high ceilings, many windows, and large attics to take up the heat. Starting in the 1960's, people started building ranch homes in coastal areas; homes on slabs with low ceilings, no real attic space, and windows too small to be comfortable without A/C. That style of house is cheap, but it is also the kind most prone to serious damage anytime you get floodwater, and if water does come in, there is no where to go but your roof. I used to know a man who lived in a very flood-prone area in-between the point where two rivers converge; his house was completely designed to handle the frequent flooding. He had winch-pallets under all the major appliances so that he could hoist them up to the ceiling, his attic is large and finished, so that it is possible to go up there to avoid high water, and the house itself is built on 9 foot piers which are sunk 30 feet deep. He can ride out almost anything in that house, and usually does.
PS; One other thing. Let's be clear on what a mandatory evacuation represents in a hurricane. It is a legal term, and what it means is that, for their safety, first responders will not be sent into the evac zone while the storm is active. It does NOT mean that law enforcement will knock on your door and force you out ahead of the storm. Once the storm itself has passed, first responders will go back into the area and do whatever needs to be done.
Also, the thing about Katrina and the marker-on-the-arm was not something that was broadcast on the news before the storm. It's a scare tactic used by cops who are going door-to-door, usually in smaller beach communities. If no cop showed up at your house, then no one handed you a marker and told you to what to write. Reporters later heard about it and mentioned it, but that was after the flood had already hit.
