They still have routes through all of those cities, and the reason it's circuitous to get from Jacksonville to New Orleans is that there's a line that goes directly there but it's suspended. They're making efforts to restore it, but the process is unsurprisingly full of politics and bureaucracy.
The line is "suspended" since Hurricane Katrina hit NO and even with the new infrastructure funding is not set to be re-opened. 18 years later it's fair to say we've moved past "suspended".
