49 does not need to be extended to New Orleans. I-10 already does the job between Lafayette and NOLA. If they're hellbent on building 49 southward, have it end at Fort Smith on 40, and renumber the Louisiana portion to I-51 or I-53.
Actually I-10 really doesn't do the job. It certainly does not serve all the traffic needs for both the I-10 corridor and the US-90 corridor farther South.
I-10 East of Lafayette to New Orleans becomes its own bottleneck of sorts, thanks to those long, aging bridges with only 2 lanes in each direction. That capacity is barely efficient for I-10 traffic loads while weather and traffic conditions are good. It's another matter if a hurricane is moving toward the area and big numbers of people are trying to get the hell out of Dodge.
One of the selling points of I-49 South is an alternative hurricane evacuation route. The Westbank side of the New Orleans metro is home to a lot of people. A completed I-49 to those Westbank suburbs would give those folks a good alternate exit route. There's only 2 bridges across the Mississippi in the immediate New Orleans area. And the I-310 crossing is way out on the Western outskirts of the metro.
Next point: there is a hell of a lot of oil business and other kinds of commerce in far South Louisiana. The US-90 corridor is already Interstate quality along many segments and 4-laned at the minimum along the entire route between Lafayette and New Orleans. Just from the perspective of aiding business it's totally valid to convert US-90 to full Interstate quality between Lafayette and New Orleans.
As to the route numbering, well even I have my own problems with the I-49 designation. People leaving New Orleans on I-49 "North" will actually be driving more Southward. The whole segment between Lafayette and New Orleans is really more of an East-West route. Long ago I thought I-6 might be a good designation. It's possible I-6 may eventually end up linking Laredo and Corpus Christi. Hell, we could have
two I-6 routes! One in Texas and one in Louisiana.
We already have permanently separate duplicate routes for I-74, I-76, I-84, I-86, I-88
and now I-87. I-66 almost had 2 duplicate routes. I-69 will probably have a lot of separated stubs and major route segments for a very long time. I-39 would be 2 duplicate routes if not for the only triple concurrency in the whole Interstate system. I-49 has two separate routes too, but there is a realistic yet long term shot at joining those two I-49 routes.
OTOH, I prefer conservative use of Interstate route designations. I-49 as a thru-route through Lafayette points down the US-90 corridor and eventually over to New Orleans. In the end, I don't think an extension of I-49 is going to be a problem.
I think they're already planning to build it to there. The routing through Lafayette is the only hold up.
While construction hasn't begun yet on the Lafayette Connector plans are pretty advanced on it and may be final by 2021. Meanwhile construction is proceeding on other upgrades South of Lafayette. ROW is already secure on much of the US-90 corridor between Lafayette and New Orleans. A short stretch in Avondale could be tricky. Boutte & Paradis would need some kind of bypass. Interstate quality upgrades the rest of the way into Lafayette would be fairly easy due to the already wide path of US-90 and ample property set backs in place.
Honestly, I think the I-49 South project could be completed well ahead of the segment between Fort Smith and Texarkana.