[dau]

The problem with buying your own train is that you don't own the rails that you are dependent on. At least in Europe you have to submit a letter to an agency and request timeslot reservations some time in advance if you want to go for a ride.

[Symbiote]

From the article, it looks like the American way is to own a carriage or two, and attach them to a passing Amtrak passenger train. This is disruptive to Amtrak's passengers (!).

The European way is much less disruptive (the private train will fit in around whatever is already scheduled), though having to rent or own a locomotive and driver in addition to the carriage must be significantly more expensive.

I don't know about elsewhere, but in Britain there are fairly regular trips by private steam trains, or other old trains. A relative used to take these trips every few months.

People who aren't interested in the train itself can just rent an ordinary, modern train. Again in Britain, this happens for cases like a large group of football supporters (probably in the official fan club) who need to travel a long way for a match. Presumably, this isn't much different to hiring a bus with a driver.

[TylerE]

The problem is in America we don't have open access to the tracks.

They are all owned by different railroads vs the UK were they're all owned by one (formerly government) organization.

Here in the US, even if you could rent a locomotive and crew, you'd have to get permission from each individual railroad whose tracks you wanted to cross.