Also, note that it was voluntary, not a takeover, and the railroads had to BUY in. They had to pay a certain percentage of their passenger losses incurred over the prior 3 years either in-kind in the form of equipment or in $$$. That was part of Amtrak's start up capital. The stick Amtrak had was that the ICC would not consider any discontinuance petitions at all for 5 years for railroads that did not join.
Not all railroads joined:
Rock Island did not join because they couldn't afford the buy in and Amtrak did not want their beat-up equipment. They got out from under some of their runs after 1975, and, of course, the bankruptcy finished off any remainders.
D&RGW did not join because they did not want Amtrak dictating schedules over their single track mountain railroad (and, in fact, they operated the Rio Grande Zephyr as a 2nd Class train, so 1st Class hot freights had rights over it, something that they could not have done with the standard Amtrak contract of the time). Amtrak and Rio Grande finally negotiated a modified contract in 1983. Amtrak wanted on the D&RGW badly. D&RGW had the ICC turn down all their discontinuance petitions, even the partial one just between Grand Junction and Salt Lake City where they had very low ridership. I was on it one time when there were fewer than 10 people onboard departing Salt Lake City. A bunch of people got on at Grand Junction, and that train was completely full departing Glenwood Springs.
Southern did not join because they felt they could run their remaining trains as a class act with minimum losses, having already successfully decimated most of their passenger services under Brosnan. They got rid of the trains other than the Southern Crescent after 1975 and turned that over to Amtrak in 1979.
There was a relatively small RR in the South that did not join (Central of GA?), but were able to discontinue after 1975.
Santa Fe came very close to not joining. They only signed the Amtrak contract in the middle of April 1971, just a couple weeks before Amday. John Shedd is on the record having said that had Santa Fe been allowed to cut back to the trains that Amtrak itself kept (Super Chief/El Capitan and the San Diegans) and dropped the ones Amtrak did (San Francisco Chief, the former Grand Canyon-23/24, the Tulsan, and the Denver-La Junta connecting train), he could have convinced the Board to stay out. That wasn't the way the legislation was written, though. As it was, they estimated that operating losses from running all the passenger trains would have wiped out all the freight profits by 1975. And Santa Fe actually wanted to stay in the business, but on their terms.