If Memphis is not the destination, and not a mandatory stop on the trip, I will work pretty hard to avoid it. The problem is not really Memphis, but all that is going on with merged traffic and never finished construction west of Memphis, where I-55 and I-40 run together.
Then, for east-west traffic, there is still the problem of I-40 being rebuilt between Hazen and Brinkley. From Little Rock to Gulf Coast there is the US-65 option, going a short distance east on something (I-20 works, not ideal) to reconnect to I-55 if going to NOLA, or using US-49 from Jackson if going to Biloxi.
Nashville to NOLA there is the I-65/I-20 option, or Natchez Trace Parkway for a leisurely non-commercial drive.
NOLA to St Louis or Chicago, you are sort of stuck. Suck it in, stay on I-55 through W Memphis. All those big trucks get through that bottle neck eventually, it just make me impatient, and a bit nervous when they try squeezing into my lane.