The "solution" on paper is easy, fewer delays and better OTP. The #1 problem with transfers is obviously connections and if you have better OTP missed connections are less of an issue. I'm guessing east to west is more reliable than the other way around. I remember connecting from the LSL to the CZ a couple years ago. The LSL was late getting into CHI and the CZ departure time was moved up and while I felt rushed I still made it. On the other hand, I've taken the SWC back to CHI and I don't remember any significant delays getting into CHI. On the other hand if you have better OTP and fewer delays the idea of coast to coast travel becomes more feasible. Right now you hate to see the passenger from the SWC miss the LSL and get stranded overnight in CHI but if you delay the LSL the passengers getting on in CHI are delayed as well. As long as more people get on in CHI than transfer, the lesser of two evils is the current situation.
In terms of west to east, ideally the western trains would arrive a lot earlier than they do. But you'd like to keep the SWC leaving LAX after the rush hour and it would be hard to leave EMY any earlier, especially considering the Thruway connections from San Fran. It's hard to push the LSL any later. Maybe the CL could be moved back an hour or two although that could mess with the CL-SM or CL-Crescent connections (I think the CL-SS is tight now as is and isn't guaranteed north to west anyway).
Another "solution" is increased service. Missed connections on planes are more tolerable because of missed connections. But most areas have just one train to/from CHI. If you miss the CL and were booked to WAS, you could transfer in NYP to WAS but 48-187 doesn't get to WAS until after midnight and that assumes the LSL isn't delayed and if you were going CHI-PGH you might as well stay in CHI until the next CL. Imagine if there are two LSL's or a LSL and a BL. Ideally one would leave in the morning and one in the evening. So if you miss the connection from the west you're still stranded overnight but you'd leave CHI a lot earlier.
I would say the transfer in CHI isn't bad assuming a reasonable connection time and no missed connection (a big assumption). It's at a good time, the station is pretty nice with a lot of food options in the food court as well as some other food places outside the station. I believe I once went to and went up the Willis Tower in the between the SWC and TR. Of course the transfer in PGH is horribly timed and the station is an Amshack. In an ideal world, the connection window should be 2 hours going west and 4 hours east rather than the reverse as is the case today. There is talk about a second Pennsylvanian. If it were timed well it would give passengers another option if they miss the current CL-Pennsylvanian transfer (which did happen the day I was on the CL).
In theory the CL-NER (for CHI to BAL, WIL, PHL, and NJ) is the one where the missed connection would cause the least inconvenience because there are multiple trains. The problem there is rebooking and as jebr suggested fixing the IT system should help there. In reality, once Amtrak realizes the CL or similar trains will be delayed they should be working with passengers they know will miss their connections while they are still on the train rather than force them to wait in a long line in WAS Union Station (since I was working on a RailPass I wasn't able to change my connection online). I know they did set up a bus to carry missed Pennsylvanian passengers. This also applies to other major transfer points. If the SWC/CZ miss the CL connection, you know the line in CHI will be even longer. I can't the only one here that went through hell waiting in line after they miss a connection.
The solutions are easy in theory but difficult in practice.
Did I tell you how much I hate transfers? If I had a one seat ride from Bucks County to the Phillies stadium, I might take it. I'm not aware of one. Those of you in Philly might have heard of Fern Rock Transportation Center. It's a way to transfer between regional lines to the suburbs and the Broad Street Line to the stadium. But it's outdoors which is great during the day when it's warm. One time I came back from a 76ers game using the BSL to Regional Rails. It was January and at night. Since Regional Rails have roughly hourly service you can wait up to an hour if you time it badly. An hour may not mean much in an Amtrak trip but this is outdoors in January in the dark with no security present and I don't believe it's that safe a neighborhood. Well I remember the wait was long enough that in order to stay warm, I spent time in an elevator at Fern Rock. Now I just drive down. That's a one seat ride.
Broadway Limited (CHI-Harrisburg, PA)
Three Rivers (Harrisburg, PA-CHI, Altoona, PA-CHI, PHL-CHI)
Capitol Limited (CHI-WAS)
Lake Short Limited (NYP-CHI)
Silver Meteor (PHL-ORL)
Southwest Chief (CHI-LAX)
California Zephyr (CHI-SLC, SLC-EMY)
City of New Orleans and/or Illini (CHI-Champaign, IL)
Bring back the Broadway Limited (or Three Rivers or any Chicago-Pittsburgh-Philly train)!