Last i checked Ayn Rand never advocated for private usage of eminent domain.
I am sorry, but eminent domain is never “private”. In some cases a public use may involve private contractors, for example building the Golden Gate Bridge.
The Golden Gate Bridge construction project was carried out by the McClintic-Marshall Construction Co., a subsidiary of Bethlehem Steel Corporation founded by Howard H. McClintic and Charles D. Marshall, both of Lehigh University.
We never really heard how those rails got laid in Atlas Shrugged, but there may have been some eminent domain.
There have been some instances where a public entity wanted to use eminent domain and leave the results in private hands but in these cases a vastly important public need must also be involved. (Such as the construction of a hotel and thousands of jobs.) These cases need to be reviewed more carefully and various public bodies are developing restrictions against this practice. But the public basis still must be confirmed.