can it be true that for 100 years they have shipped to a terminal somewhere in the middle of the country, dumped cars onto sidings or switching yards, and then waited for some other company to come along and hook them up and carry on?

I'm not an expert either, but as I understand it it's uncommon for an intact train to go coast to coast. What happens is that train with cars ABCDEFGHIJKLMN leaves the east coast, then in Omaha is broken up into a second train with cars ACDFJLM (plus cars OPQRS from some other train from, say, Minneapolis)) and sent on to Seattle, and cars BEGHIKN (plus TUVWXYZ) are sent off on a new train to LA.

There's a fun observation tower where you can watch all this stuff in the Omaha switching yard that makes for a good Tourist Nerd Stop next time you're traveling I-80

How they did this with any approach to efficiency in the days of hand-operated switches and paper ledgers is beyond me. I have visions of fifty tons of Florida oranges accidentally being sent off to Denver instead of Chicago

--sutton