A similar issue came up recently when the National Speleological Society decided to stop printing members manuals. There was definitely an outcry and some of the points I think were valid. On the other hand, a society dedicated to among other things, conservation, had a hard time justifying sending manuals to members, a majority of whom would toss them. The main argument is, "people can still download the PDF and print it." Which is true.
That said, I recommended to them, and I would to ANY such society and also to Amtrak to have SOME form of printed document, even if it's a very limited distribution and that's for archival and research purposes.
I've seen multiple articles in the NSS News where someone dug through archives to find the history of some member or related information.
Besides just current railfans, 3 decades from now railfans and legitimate researchers are going to want copies of timetables. An electronic only version is nice because it's always current, but, unless steps are taken, that's also a HUGE issue because it's ONLY current. Yes, current railfans may print out copies and hold on to them, but that's not quite the same.
At least with the NSS Membership manual, I'm about 95% certain that not only does the NSS Headquarters have printed manuals going back to inception, so would many research libraries. These are an important part of our history and will continue to be so.
(An example of non-railfan research could be the case of Congressional Staff trying to gather data to support a bill to speed up the NEC, and wanting to compare train times over the years. Without easily accessible historical records, this ability will be compromised.)
So, I don't think Amtrak needs to make 100s of thousands of copies of their timetables available, only to be tossed after one use, but I do think for several reasons, if they're not, they should be taking steps to ensure research libraries and other areas DO have them, and that individuals can print them for their own needs.