Take a closer look at the Lincoln and Missouri River Runner schedules.
https://www.amtrak.com/content/dam/proj ... 091317.pdf
Both morning trains leaving St. Louis do so before the Texas Eagle arrives, even when it is on time. While very early in the morning for a St. Louis departure, these trains are not subsidized by Missouri or St. Louis. They are subsidized by Illinois, and their arrival time into Chicago is early enough sp passengers transferring to other trains can make them. Simply stating, Illinois is subsiding trains at times it prefers, dang those from St. Louis who must wake up early to catch an early train. The eastbound morning Missouri River Runner does not reach St. Louis until after noon, but it continues onwards to Chicago. There's a later evening train from St. Louis to Chicago.
My point, is that there is not a locomotive or crew available in St Louis for whatever spare cars are in St. Louis to head for Chicago for an unscheduled train in lieu of the Texas Eagle. The locomotive available is for the westbound Missouri River Runner heading to Kansas City. So, if you steal this locomotive and rolling stock to head for Chicago, there is nothing left to head to Kansas City. It's this train that also returns to St. Louis that evening from Kansas City, so that train is also missing equipment because it is now in Chicago.
Meanwhile when the late northbound Texas Eagle arrives in St. louis after 7:55 sm, there will not be a crew available until 4:00 pm for the next northbound Lincoln service train, 8 hours later. Stealing it's scheduled crew for an unscheduled train could make it up to another 8 hours later into Chicago, eliminating any opportunity for its transferring passengers to make them.
I do not schedule the Lincoln service trains, and I can see why you would like to see one morning departure from St. Louis after the Texas Eagle. But obviously, that is not what Illinois wants.
Here's my solution for avoiding a very late Texas Eagle and getting to Chicago before dinner, take the evening train to Chicago the night before. Book a room at a hotel, and you will be in Chicago when you wake up the next morning.
Instead of complaining about the train schedules, change yours.