Look at it this way, Asheville gets more tourism but there's been almost nothing added to the highway system there in the past 20 years (for a variety of reasons), so as least you're not that far behind in catching up with traffic numbers.
In fairness, about 20 miles of I-26 between Asheville and Hendersonville were recently placed under construction widening the highway from 4 to 8 lanes in the northern section, and from 4 to 6 lanes in the southern section.
The construction of I-26 north of Mars Hill was completed back in 2003, less than 20 years ago.
Asheville is a larger metro area than Greenville overall, and has more traffic demands both thru and local having both I-26 and I-40 passing thru the area. Older, substandard freeways that aren't adequate, urban routes, etc. then there's the cluster *** that the I-26 / I-240 junction is.
Greenville's freeway system is relatively new compared to Asheville and plenty adequate for the traffic it sees.
Keep in mind, Greenville has gotten a decent amount of access to/from improvements over the past 20 years. The completion of the US-64 freeway to Williamston and the widening of US-13 to 4-lanes between Greenville and US-64 has opened up a new 4-lane route to Hampton Roads and Northeastern North Carolina, the completion of the US-264 freeway around Wilson has completed a 4-lane freeway route between Greenville, I-95 (in both directions), and Raleigh, and effectively then to I-85 and I-40. Greenville has better freeway connections than Hampton Roads does when it comes to connections to interstate highways such as I-95 South, I-85 South, and I-40 West, and it's far smaller than Hampton Roads.
My opinion is the local road projects should be accelerated in Greenville, and in the future as growth continues, construction of a southeastern loop may be warranted, but that's about it. There's no need for miles upon miles of rural freeway construction to supplement existing 4-lane routes that only connect to minor population centers, such as US-64 to US-70, or US-264 to Washington. There may be a local desire, and that's great, but it's going to be far low of a priority funding wise. If the funding comes around after all the other issues in the state have been dealt with, then that's great, but these local interstate concepts can only be realistically A) not built and left as is with 4-lane rural highways, or B) built in many segments, piece by piece.