Why would they run the cafe to Chicago? Doesn't the Capitol already have a cafe? You wouldn't need two between Pittsburgh and Chicago...
To provide food service to the single level portion without the need to climb stairs. Since it needs just one additional cafe, of which there is quite an abundance, it is a non-issue really. If enough Club-Cafes can be found, it also opens up the possibility of BC service.
How often have you seen Amtrak place two cafe or lounge cars within the same consist? More likely, the intention would be to run the Capitol Limited with only a dining car - no Sightseer Lounge - and the single-level cafe/lounge sufficing for lounge space. Other trains which split en route generally operate with the diner in one section and the lounge to the alternate destination (Empire Builder, Lake Shore Limited). Climbing stairs isn't really an issue (aside from mobility impairments, for which provision is made) and Amtrak has operated split-level trains before (Heritage sleepers and Superliner coaches).
I actually happened to have traveled with the guy who wrote the PIP on one of my WAS - CHI trips on the Cap and discussed this matter as we happened to be seated at the same table for dinner. (I had a roomette two doors down from his in the Trans-Dorm too) He has since been let go by Amtrak. I was just reporting on his take. Of course others can come up with other reasons.