I - 24's number of lanes is inadequate from exit 81 in Murfreesboro to exit 185 in Chattanooga save for the few miles on the eastern side of Monteagle.
Not true...it's adequate between Murfreesboro and I-59. At I-59 is where you have justification to widen I-24 east into Chattanooga.
I drive the interstate frequently, and it could certainly use the widening. Plus I - 75 from Naples to Chattanooga is either 6+ lanes (or being widened to 6+ lanes), as is I - 65 throughout the length of Kentucky. Logically, that says to me that I - 24 from Chattanooga to Nashville as well as I - 65 from Nashville to the Kentucky line could stand to be 6+ lanes.
The Chicago - Atlanta and Detroit - Atlanta truck routes are two of the busiest, and they converge in Chattanooga. I - 24's number of lanes is inadequate from exit 81 in Murfreesboro to exit 185 in Chattanooga save for the few miles on the eastern side of Monteagle. Either the road needs to be widened to 6 lanes or two new interstates need to be built, one as a beltway around Chattanooga on the south, east, and north sides, and one from Hwy 27 in Soddy - Daisy, TN to I - 65 in Cave City, KY through Cookeville, TN, the Soddy - Daisy - Cookeville section being an upgrade of Hwy 111.
I don't think the route into Kentucky would need to be an interstate. There are plans to improve KY 90 in spots from Burkesville to Glasgow. Instead of taking TN 111, traffic could use the TN 56-53 corridor north from I-40 to reach Kentucky, then KY 61 to KY 90. Might not be an interstate, but most is already an improved route.
But an interstate (or toll road, such as a turnpike) would be justified. Shaving 75 miles off the route through Nashville for travelers between Atlanta, Miami, Tampa, Orlando, Jacksonville, and Chattanooga in the south to Chicago, Indianapolis, Milwaukee, and Louisville in the north, which combined the metropolitan areas have a little more than 35 million population. If the road costs $3.5 billion to build (may be higher due to rugged terrain), that's $100 per person who could potentially use it while driving south to north or north to south. If a vehicle gets 25 miles to the gallon (which many get less than that), the route through Nashville costs approximately an extra $12 in gasoline, not to mention the extra driving time, which would be OVER an hour considering downtown Nashville and Monteagle easily. Charge that $12 in tolls, most people would gladly fork over that to save the driving time plus gasoline. If everyone in those 10 metropolitan areas used the highway 9 times, it'd pay for itself using the $3.5 billion figure.