In fact, why the heck aren't trains autonomous? It would seem like they'd be the low-hanging fruit.
In a sense, trains have become increasingly automated over the years. Heck, air brakes in the 1890s were a big step since a split train would go into full emergency(both ends) when the brake pipes came apart.
The engineer still has to watch signals, but increasingly they don't even have to "watch" for them thanks to in-cab signaling. Signaling itself has been at least semi-autonomous for years since you effectively use the train on the track as a giant electric switch to tell you that a block is occupied. Major yards used to have huge signal towers full of indicators, levers, and other information and controls-now when there is a signal tower there are often just one or tow guys up there to make sure nothing goes wrong. Many locomotives now will-again-dump the brakes if the train passes a red signal.
The caboose is now gone for all but local use(I still see a few cruising around the yards here). The conductor used to be back there to monitor the status of the train, report on things like brake pressure and how things were moving(a 100 car train does not behave the same along its entire length) as well as be able to apply brakes at the end of the train if needed(due to the way air brakes work, a brake application in the caboose will propogate the whole length of the train, although you might inadvertently tear the train in half). The caboose was also a visual indicator of the end of the train. Now all of those functions are done by an electronic box hanging off the last car with a flashing red light, sensors to monitor movement and brakes, and the ability to open the brake line. The conductor now sits in the cab(the former "fireman" seat that was retained well into the diesel era) to monitor that kind of stuff.
Getting a train moving-in the diesel and electric era-is not that complicated. There's a "reverse" lever that sets the direction of travel and then a throttle with 9 positions(notches). 0 is no power to the traction motors, while 1-8 are varying levels of power.
The thing that keeps things from being fully autonomous is slack management. Basically, slack is the free play between couplers and it is quite significant on long trains. When you start a train, you are "stretching" it, and this is important because the locomotive is really only "starting" one car at a time. Where it comes into play most notably is when a long train is traveling over uneven terrain and you can have the train both stretched and bunched at various locations throughout it. Poor management of this can lead to a broken train or derailment.
Once again, it's important when stopping. Braking(at least in the US) still works on the same basic Westinghouse patent that's well over 100 years old, and brakes are applied on individual cars by decreasing the pressure in the train brake line. Once again, on a train that's a couple of miles long, it will take a while for a pressure reduction made in the locomotive to propogate all the way to the end of the train. If the brakes are applied too fast, the end of the train can be moving much faster than the beginning, and you get the type of derailment where the train turns into an accordion.
Many braking decisions are still made by the engineer according to conditions and specifics of the train, and like take off and landing in an airplane, it's pretty darn hard to automate them.