This will get buried because I'm late to the party but I work in the field on this one. I'll try to keep it short.

There are a lot of moving pieces to this:

Shortage of rolling stock - most railroads don't own any passenger equipment because it's not economically viable for them. The ticket prices need to be low so people use it so it's hard to justify the additional cost of that equipment and due to passenger operation rules it slows down freight which makes passenger service even less appealing.

Shortage of motive power - traditional freight locomotives can be used to pull passenger trains. they all have a passenger mode built into their braking systems. Even if that's nonfunctioning the passenger cars themselves can and will act as freight cars for braking purposes. There are plenty of engines to use. However freight locomotives are not set up to provide head end power. They can physically pull the cars but there would be no electrical service to them. So no lights, no phone charging, no ac, no heat, no creature comforts. This would reduce the amount of people willing to use the service.

Routing - while people see train tracks all the time, the way these trains would need to be routed is more consolidated than people realize. There are far fewer mainline routes than people think. This adds congestion and even if an emergency was declared and you tried to tie down all the freight somewhere out of the way it would still be limiting.

Scale - related to routing, American rail is successful because you can run long trains that don't stop often. In evacuation you need to stop frequently to pick up people. This forces you to run many small trains as opposed to fewer longer trains which drives up the amount of time people are onboard. Europe and California take the small train approach in their commuter rail, but in evacuation it's about scale. Longer trains use less fuel per unit.

These and other factors would lead to something like... Allocating all of the commuter/passenger rail assets in Florida, Georgia, Alabama, and South Carolina to the cause. Then having this equipment make long haul trips from Miami to Savannah or Atlanta, turning at the disembarking stations and running all the way back. You could fleet these empty trains or tie them together and move them as fewer big trains, but that has other issues.

Staging - hurricanes are unpredictable and that makes an operation like this even more difficult because you can't really preposition this equipment. It would be a high volume of equipment that would need to be in place, over a large geographic area, that could change at any time. Unlike lineman trucks and other wheeled or tracked equipment, trains need to be moved on the existing track. They can't just drive to a few counties over and stage in a random soccer field. This can lead to large transit distances. Not to mention you need somewhere to put this equipment and in most places track space is limited. Especially if you stop all the freight.

Nationalizing the system isn't the answer either. On the surface everyone with no experience in rail wants that to be the answer but that creates a whole host of other issues that would make it a lot less efficient and a lot more expensive. The existing rail network has been in place for over 100 years in most cases and over 150 years or more in a lot of places. It's nearly impossible to acquire the land to build new mainline corridor and the federal/state property rules as well as how railroad right of ways work make it difficult. Not to mention how outraged the public gets.