As far as BNSF is concerned it would be better for Amtrak to stay on the current route. But only if someone else pays to maintain it. Then they have the route to use when they want at better speeds, don't have to deal with Amtrak on the transcontinental, and don't have to pay very much.
The question is not whether it is or isn't better for Amtrak to stay on its present route, but whether or not BNSF thinks it is. We really have no way of knowing the reality of this. The question is whether or not BNSF has made that conclusion from their studies, and their studies will include a lot of information that are simply not publically available, and much of which would probably be incomprehensible to most people, anyway.
My own opinion is that if they truly want to keep the SWC on its current route, then there needs to be the decision to get out there and relay the thing completely with new or truly good relay CWR and reinstate the ATC/ATS whatever they had and replace the essentially musuem quality signal system.
There is a precedent to shifting the train. The City of New Orleans between Memphis and Jacdson MS being it. The train was on the traditional passenger route through Grenada and Winona MS and did a fairly good business at these and other stops. However, the route had a severe arrears in maintenance, needing a near complete rail relay among other things. The traditional freight route was given signals and a 79 mph speed limit and the CNO shifted. The Grenada route had the signal system turned off and has deteriorated since. It may have by now been partly sold or abandoned. In this casse there was only one town of any significance on the replacement route, Yazoo City. What is being discussed for the Southwest Chief is the same sort of thing, exactly, only on a larger scale.