I don't understand how you assess the validity of your statement. Since you are talking about London as a world-class system, surely you should include Paris, Hong Kong, and Moscow. These were not "originally built by private companies."

A few days ago, CNN listed Hong Kong, Seoul, Singapore, London, Paris, Madrid, NYC, Tokyo, and Guangzhou as being in the top list of subway systems. At least some of those were started either by the government or by a government owned/funded company.

The US has a long history of preferring business solutions over government ones. Compare to 1800s France where large-scale engineering projects were seen as part of the government's domain. I therefore suspect that your observation reflects a US-centric view, where the default view seems to be that the government is incapable.

Also, there's a possible selection error. If all of the worst systems were "originally built by private companies" and only 40% of the world-class systems were done that way, then wouldn't that suggest that early government involvement leads to better systems?

Without that information, it's very hard to use your observation to make any sort of informed decision.