If they are not mobile then look for something other than train travel.
That's a bit harsh. Amtrak by law is required to make reasonable accommodation for passengers with mobility disabilities, and most Amtrak staff I've encountered (when traveling with my elderly, mobility-impaired father) have been very graciously helpful with this.
Train travel is ideal for folks with certain kinds of mobility problems: You can see a lot without needing to walk very far, and even if you ordinarily use a cane for balance you might not need it on the train--the corridors are narrow, and there are ample things to grab onto to steady oneself along the way.
While I do think that train travel can be great for those with mobility problems, there are a couple points in your post that I don't totally agree with:
While Amtrak is required to make reasonable accommodation for pax with impaired mobility, I've found that that's not always the case. Multiple times, I've seen Amtrak fail to provide necessary equipment (ramps, carts, etc) and assistance to passengers trying to board or disembark from the train. Sometimes the staff aren't helpful, other times the station just doesn't have the necessary stuff onsite.
I do also sort of disagree that passengers who need canes might not need them as much when moving about a moving train. I feel like the sudden motion and swaying of the train really more than compensates for the fact that you have plenty of stuff to grab on to as you walk though it. I just feel like someone who usually needs a cane might as well keep using it while on board. Just my take.