The crux of it is "viable" though. It's viable in the same way taking a cruise ship from LA to Miami is a viable form of transportation. You can do it, it does work, but it's more something you take because of the journey than as an effective way to travel itself. I'd also be shocked if it wasn't running at a pretty substantial subsidy.
Sure, but most airports are being used. If you're subsidizing it heavily and it's still a novelty instead of a part of regular infrastructure, then it's a different story. I was checking quick, and Amtrak is claiming that the train from LA to Chicago this Friday is 100% booked, but I'm unsure how many travelers that is, and they're only running the one train that day. It also takes nearly 2 days.
I'm not against subsidizing train travel, but you should be getting something for it. You could decide to add a train between any two places and dump money into it until it's cheap enough to fill up. The question is if you're causing people to take the train who would have otherwise driven/flown, or if you're just subsidizing a new market.
I don't live in either city, but the concept of taking one of the other long-haul Amtrak lines from Chicago to Seattle has seemed interesting to me. It's not that expensive and it would be quite scenic. That said, if I took it, I'd be flying to Chicago, then taking the train, and then flying back home from Seattle. That's not replacing a flight/drive, it's creating net new flights. Is that the sort of train line that we should be subsiding the existence of? I can see the value of doing it as a matter of culture and history, but if the goal is to reduce the carbon emissions of flying and driving, it may actually be counterproductive.
