When I was able to take my bike on a train, it was the Amtrak Pacific Surfliner, from Old Town (OLT) to San Clemente (SNP). One time I handed my bike up to a porter in I guess a cargo car (I didn't get to go up and see inside), the other time there was a car where half of the seats were removed and bike racks installed.

Around here it is more common for commuters to ride "The Coaster", a commuter train that runs between Oceanside and downtown San Diego, but I've never been on it and don't know their rules for bikes.

I also lived in Reading UK for two years and daily commuted to Paddington (NW London), and it was often very crowded and I only vaguely recall the occasional folder. I was not a cyclist back then, so I wasn't really so aware, but you're probably right, it's uncommon to be able to take full-size bikes on trains. Although it seems a shame, it should be easy to put racks on the front or back like on buses.