Well, the option thus far has been "build taller/bigger levies". Which is why the river can get to 14 feet above flood stage and still not be flooding. When the walls still aren't big enough, they make temporary sandbag walls on top of the walls.
All this does though, is forestall the problem and in the end, make it worse because you're dealing with that much more water downstream.
By the time it gets to Louisiana, you're talking about engineering on a mega-scale. One of the big concerns (and a large part of the decision to open the Morganza spillway) is what's known as the
Old River Control Structure, a system of floodgates that works to divert water away from the Atchafalaya River and into the Mississippi.
Why? Because Mother Nature doesn't want the mouth of the Mississippi to stay in New Orleans. Over time, natural dynamics have increased the flow into the Atchafalaya (which branches off of the Mississippi in northern Louisiana and heads in a much steeper and more direct path to the Gulf of Mexico. If allowed to do so, the port facilities in places like New Orleans would eventually not really work, and the new Mississippi Delta would be hundreds of miles to the west. River traffic would be changed and billions of dollars in commerce would bypass the Big Easy.
The problem is, if the Old River Control Structure fails, then this change will happen anyways. All at once. The damage would be unbelievable, reshaping the Louisiana coastline and utterly submerging chunks of south central Louisiana. New Orleans, after a few years of sedimentation and lower flow, would be sitting in a giant mud flat.
But going back to the original question, so what? Should we continue to try and essentially terraform one of the largest rivers on the planet, at considerable cost and knowing that it only forestalls future problems just like this, only bigger? Or do we at some point decide to let Nature have its way, evacuate a huge area of all habitation, and let events play out?
Should we start trying to reduce the levees and accept a certain measure of flooding, in the attempt to prevent it larger floods later? Should states downriver get any kind of compensation from states upriver, whose levees contributed to the severity of their more southerly neighbors' plight?
There's a similar collective action problem along beachfront properties, where erosion caused by longshore waves picks up sand from your chunk of beach and transports it down-current to your neighbor's beach. To combat this, you can build a
groyne, which is a kind of wall used to trap sand movement and create stable beach. However, this results in an even higher rate of erosion on the backside of the groyne. So your neighbor downstream now has to build an even larger groyne to retain his beach. His neighbor has to build one even bigger than that, and so forth. Once you get to the end of the series, the amount of erosion behind the last (terminal) groyne can be severe, a condition known as terminal groyne syndrome.
The solutions have been varied. In North Carolina, they just flat-out outlawed groynes and basically said, "Beach erosion is just part of owning a beach house." You're allowed to truck in a certain amount of sand per year, IIRC, but as the Outer Banks are migrating islands, eventually that house on the regressing side of the island is going to be underwater. Them's just the breaks.
In South Carolina, they allowed groynes, so in heavily built-up places like Myrtle Beach, you have condos and hotels on the beach with ridiculously long groynes so that "their" beach is assured, and I can only imagine what the backcut erosion is like once you get past the heavily commercial areas.
EDIT: Here's a map of the projected flooding if/when they open the Morganza spillway at 50%, to give you an idea of the scale involved: