An interstate through Lynchburg would've eliminated the I-64 East to I-81 North (and vice versa) and I-64 West to I-81 North (and vice versa) connections though as it would've followed US-220 down to near Roanoke, then the US-460 / US-360 corridor eastward.
A US-60 routing would be roughly the same distance as the current US-250 routing is.
It's not so much distance as it is travel time. Taking U.S. 460 to Lynchburg and beyond, then U.S. 360 into Richmond involves a number of locations with traffic lights, lower speed limits, and traffic that increase travel time. A limited-access highway all the way between I-81 (somewhere between Troutville and Lexington) and Richmond would decrease travel time.
A limited-access highway along US-460 with a posted speed limit of 70 mph between I-81 north of Roanoke and the VA-288 beltway would decrease about 30 minutes of travel time off of the US-460 routing, resulting in being about 10 to 15 minutes faster than present-day I-64.
It would, however, eliminate connections from I-64 West to I-81 North, and I-64 East to I-81 North that would have to be handled by arterial corridors.
Charlottesville and Lynchburg would switch roles, with Lynchburg being on an east-west interstate highway and Charlottesville with none. There would likely be more support for a US-29 freeway upgrade near Charlottesville since they would have no access, unlike today where they don't seem to care for anything besides I-64, opposing and rejecting any US-29 freeway concept, whereas Lynchburg on a southern I-64 may not have as much support for a north-south freeway, unlike today where they have supported a US-29 freeway concept from Lynchburg to North Carolina, and had little opposition to the 2005 Madison Heights Bypass.
If a US-460 routing was chosen for I-64, US-250 would've likely been dualized to a non-limited-access 4 lane highway in the manner that US-460 and US-360 were throughout the 1960s and 1970s, with freeway bypasses near Charlottesville and Waynesboro
(or rather a traffic light infested bypass near Waynesboro, and either a substandard 55 mph (like US-29) freeway near Charlottesville, or higher quality 65 mph freeway (like US-460 near Lynchburg)), a twisty, narrow typical Virginia 4 lane through Afton Mountain, and a toll road / freeway built out to at least Short Pump in the manner that the Powhite Pkwy was.