On further consideration, I can probably predict most of the arguments for the selected alignment. This was before NEPA, so cost and traffic would likely be the major considerations (notwithstanding political aspects that may be brought up by a congressman or senator).
The selected route crosses the Tennessee River and Cumberland River BELOW Kentucky Lake and Lake Barkley. You would need bridges over rivers vs long causeways plus bridges over the lakes. That might have been the deal breaker for the other routes shown on the map. Plus the central route doesn't really serve any towns between Hopkinsville and Paducah. Another advantage for the selected route is probaby that it better connects with the Western Kentucky Parkway, although I am not sure if that would be a primary advantage to the Feds, except that it might attract more traffic to that route.
When considering a connection through Illinois to I-57 versus a connection through Missouri to I-55, the probable advantages for the selected route are possibly a lower cost for an Ohio River crossing versus an Mississippi River crossing, providing an alternate route to Chicago via I-57 as well as the indirect route to St. Louis, which would probably mean higher traffic volumes. Needless to say, a connection to I-55 would had provided less of an indirect route to St. Louis, since only one additonal interstate would be used, instead of two. However, I figure Paducah saw that the Illinois route would serve it better than a route into Missouri.