The route is pretty flat overall, but there's still the problem of:
1. Population. Chicago has nowhere near the population of Boston + NYC + DC, and going from the Midwest to Denver Chicago is only really in line for people coming from northern Ohio/Indiana and the lower peninsula of Michigan. That adds some population, but you're still nowhere near the population of the Northeast megaopolis.
2. Snowbirds, or more broadly stated, temporarily relocating people. The Auto Train costs around $400 to haul a vehicle round trip, saver coach round trip is $190, and a roomette round trip for one person seems to settle around $530 (including the one person's rail fare.) Flights on Spirit are typically under $200 round trip, and legacy airlines are closer to $400 round trip on more expensive days. That means a car rental would have to be over $200 for it to break even to bring your own car if you took coach and got the saver fare, or over $550 if you went for the roomette. That'd be even higher if you took Spirit, Frontier, or got a good deal on a legacy airline ticket. For a week or two, it'll almost certainly make more sense to rent a car. The savings only really start adding up if you're in the area for longer than a few weeks, because then it's significantly cheaper to haul your own vehicle than to pay for a rental. That's why snowbirds are such a lucrative market for the Auto Train; they will typically be relocating for a few months so renting a car while at their destination is a lot more expensive proposition than someone visiting for even a couple weeks.
3. Traffic and auto driving cost. For such a train to work, you'd need loading and unloading facilities for the train, which typically aren't economical to build in city centers. For the sake of argument, let's say Amtrak would choose Naperville (just outside of Chicago) and Fort Morgan (a bit outside of Denver.) That's about 900 miles; since we have a car already, the fixed cost for owning the car is sunk, so a fairer comparison would be the IRS standard rate for moving purposes (18 cents/mile), which is based on the variable costs for operating an automobile. That results in driving the vehicle costing $324 round-trip. Even with a night's stay each direction at $80ish/night and tolls at $10 each way, the cost is still around $500 round trip. That's not much less than coach for one person, but coach only gives you a seat to sleep in, where an $80 hotel room will typically give someone a decent roadside motel to sleep at for the night along the route. If there's more than one person, then the difference is quite a bit greater ($250.) There also generally isn't the traffic issues along I-80/I-76 that I-95 seems to have (at least from what I've heard about I-95.) That means that avoiding traffic isn't as much of a selling point.
Realistically, the reason that the Auto Train works is that there's enough daily demand along the I-95 corridor where people really want to have their own vehicles at the destination to make a train that takes vehicles worth running daily. That means that there's enough demand to generally cover the fixed costs (loading facilities, auto carriers, etc.) There really aren't any other corridors that fit that criteria in the United States; there's typically not enough demand on any single corridor to make it worthwhile, and there's no natural choke point or similar route to make a particular leg of it worthwhile.
