https://en.wikipedia.org/wiki/Amtrak#Formation
Of the 26 railroads still offering intercity passenger service in 1970, only six declined to join Amtrak.
It is my understanding that prior to Nixon signing the Rail Passenger Service Act of 1970, unless they had previously gone bankrupt, railroads that provided passenger service had to get permission from the federal
Interstate Commerce Commission (ICC) to discontinue passenger rail service.
Yes, they did.
The National Rail Passenger Service Act of 1970 provided a carrot and a stick for railroads to join Amtrak. The carrot was that any railroads joining Amtrak could discontinue all intercity passenger service May 1,1971 through discontinuation petitions which would be automatically approved. The stick was any railroad not joining Amtrak would not be able to submit any discontinuance petitions to the ICC until 1975.
There was a cost to joining Amtrak. The railroads would have to pay a certain percentage of their passenger losses over a set period (don't recall the details, just the overall approach) to Amtrak, that provided Amtrak's initial capital. It could be either in cash or in kind (passenger equipment).
The railroads that didn't join did not for various reasons:
Rock Island could not afford it and their equipment wasn't in good enough shape to be used for in kind.
Southern had been successful enough in pruning their passenger services that they felt they could continue their existing passenger services at minimal loss for a few years until they could again petition.
D&RGW objected to the contract requiring Amtrak to have First Class status and priority. They felt it would interfere with dispatching on their single track mountain railroad. Parenthetically, the famed RGZ was a SECOND Class train in the timetable, with many freights having priority over it.
Don't know the details about the other RRs that did not join. One thing was that NO ONE at the time thought Amtrak would last much beyond 1975, it was seen as a fig leaf and decent burial for the intercity passenger train.
WP had no motivation to join Amtrak, they no longer had passenger service, and they didn't. Amtrak did not have a choice to run over the WP even if they wanted to. My understanding is they did sign a contract that would allow Amtrak to detour over the WP in case of emergency.
Finally, I have thought for a long time that had the RRs foreseen that they'd still be hosting Amtrak in 2017, none of them would have joined Amtrak. They would have eaten the losses for a few more years, and started to petition for discontinuance when it opened up in 1975, and almost all trains would have been gone by about 1980 at the latest.