I mentioned the minor extension of I-22 to I-40 in Arkansas for a couple of reasons, none of which have anything to do with a possible Southern extension of I-57. The existing I-55 crossing of the Mississippi River stinks. It's a puny 4 lane bridge that really needs to be at least double the size. Multiplexing I-22 onto that is just worsening the problem. MS-304 coming off I-69 in Mississippi is aiming right for the big river. A new crossing could be built there. There is minimal development between the river crossing and I-40. There's a good amount of East-West traffic on I-40 headed to/from points like Atlanta. A connection getting that long haul traffic easily around Memphis would lighten the burden on the old I-40 and I-55 bridge crossings in Memphis.
On that topic of I-57, I'm happy enough with I-530 eventually being built to a junction with I-69. It a tough case to make for extending I-57 farther South into Louisiana, presumably to Monroe and then possibly Alexandria. There's lots of possible future Interstate corridors, but I don't think traffic counts are up enough to justify that one at this time. It's going to be difficult enough as it is just finishing I-49 between Fort Smith and Texarkana. And then we have all the I-14 nonsense going on. You know those efforts will try to suck away money even for a long established corridor like I-49.
I don't think I-22 needs to be extended North of I-40 along I-555, not unless there is a much bigger picture point to it. And if there was a much bigger picture corridor in the works then the I-22 number might not be acceptable. I've always thought it sucked how the Interstate highway system had no I-50. I've got a thing for diagonal Interstates, so I figured a fictional I-50 would be cool running from Jacksonville, FL to at least the Salt Lake City area, if not actually get into California somehow. I-22 would get eaten up in the process.