The link Philly posted above about the 1997-98 run of the "National Chief" (Southwest Chief + Capitol Ltd.) is quite a good read and explains why LA-WAS on a single train was and is a no-go. First, it involved an 8 hour layover in Chicago for cleaning and maintenance with the "option" to leave the train. Apart from physical disability, I can't imagine wanting to spend 8 hours sitting on a stationary train--and that impeded cleaning.
Second, sleeping PAX were not guaranteed the same bedroom or roomette on the CHI-WAS segment. Maybe it was a reservation's glitch at the time that computers today could handle--but for sure Amtrak would find other ways to inconvenience passengers going across the country, so seamless cross country train travel does not seem feasible to me. Unfortunately.