Here is an excellent illustrated history of the interface between the Red/Old/Atchafalaya River systems and the Mississippi River system.
And here's some further information on the Atchafalaya -- America's largest unknown river.
To sum up, the fact is from the Old River/Mississippi River junction, it is 175 miles to the Gulf via the Atchafalaya vs 325 miles via the current Mississippi channel.
Water seeks the shortest, thus steepest, route to sea level. If it weren't for the control structures, Morgan City would probably already be New N'awlins.
Read it all. Amazing! Thanks Okie, especially for the illustrations and photos!