While there are three roads out of New Orleans there are not three that are safe and effective for an evacuation.
I-10 East goes straight to Mississippi and would interfere with the Evacuations from the Mississippi gulf Coast.
The Causeway? Would you take a 26 mile bridge over that lake while a hurricane was approaching? One stalled car and thousands would be killed by storm surge.
That leaves I-10 West as the only viable route out of town.
While that was the main route out, there were shots of bumper-to-bumper traffic on the causeway, and I-10E was also utilized.