Just to be clear - Amtrak has no requirement for a negative COVID-19 test in order to board the train. The email that I've received in the past startled me a bit too (it was unexpected and I didn't 100% know what to expect) but it worked out fine. The line that might be tripping some people up is the "waiting for a diagnostic COVID-19 test" - which just means that if you were tested due to having COVID-19 symptoms, you need to wait for those results to come back (and ensure that you don't have COVID-19) before boarding the train.
That said, I really don't see the value of it other than perhaps some sort of cover-your-butt move from Amtrak. I'm not even sure what happens if you don't fill it out - there was one trip back in July where I didn't receive the email, so I didn't fill out the form, and nothing happened on board. It'd be just as useful for Amtrak to send a reminder out a few days before the trip reminding people not to travel when they're sick - and if the liability part is needed, have a customized link that, when pressed, confirms that they have read and understood the COVID-19 requirements for travel. Right now the link is a bit of a pain because it requires entering in reservation information (which doesn't always pull up properly when using email or phone number to verify for me) and then checking off a number of boxes - with no confirmation email sent afterwards letting you know that you've completed the form.
As for lengthening the time - unless you ask people individually when they're boarding to fill it out on the spot, there's going to be a lag time where someone could fill out the form and get sick afterwards; if I have to fill it out within 24 hours of departure, so I do it the day before 20 hours before departure, but then wake up feeling a bit sick 5 hours before departure, having the form filled out doesn't mean I should travel while feeling ill! Given that, the reminder should be sent out early enough that people will see it, yet late enough that people won't forget the rules from that email. An "initial" email 72-96 hours before departure with a "reminder" email 12 hours before departure (ideally stating whether you've confirmed that you understand the rule or not) would suffice on that front. The goal, from what I can tell, isn't to use the form as some sort of "source of truth" as to whether all the passengers are safe to travel with, but rather to be a reminder not to travel when you're sick and to wear your mask when on board.