The small towns you want the SWC to bypass don't have very many alternative transportation options other than driving, so if they lost the Chief, their economies would severely suffer because the train is their only affordable public transportation option, and is their only alternative to driving hundreds of miles to the nearest interstate highway or airport. Even in the towns that do have commercial air service, flights out of those towns are very expensive. Train service allows those in these small towns to ride to the nearest major city and fly out of the airport in that city with much lower airfares without having to drive hundreds of miles to get there.
How many of the communities that would lose intercity rail service (between Hutchinson and Lamy) do not have commercial air service or intercity bus service? Off the top of my head, Dodge City, Garden City, Hutchinson, Raton, and Trinidad do. Not sure about La Junta, Lamar, Lamy, and Las Vegas.
They may have commercial air service, but due to limited competition in those markets, it is VERY expensive compared to flights out of major cities. Having train service allows those in those small towns to have an affordable way, without the hassle of driving hundreds of miles, to get to the nearest major city airport so they can take advantage of the bigger city's lower airfares.