Weird, I would have thought for very large objects, the personal property thing wouldn't apply? Like if you're a gazillionaire and ordered something like a huge bronze that could not move by road? Though maybe those sorts of things would be owned by the contractor or whatever you'd hire to move\order the thing from. I presume that RR's don't want to touch this because of the insane liability they'd incur if something like that got damaged? Or does it have to do with the legal definitions of shippers?
It occurs to me that this may also one of the reasons why, back in the old days, there was alot of mail & baggage traffic, since small businesses & the general public would have been able to send LCL packages that way. Now that the freight carriers are out of that business, it's no longer possible.
I want to say I've seen pictures of helicopters, non-privately owned, on flatcars under tarps somewhere before. I suppose one of the smaller, 1950s ones might, disassembled, might also be able to be packed in a auto boxcar which would protect it in transit...?