Did Ayn Rand sincerely believe that Objectivism would be good for mankind?

Interesting that you should bring that up - I’ve just responded to someone else touting Kerala as a communist success. I’ll quote that in its entirety.

Note also that the communist party has been powerful in Kerala, but they have by no means swept all elections. In fact, since 1982, they’ve effectively alternated power with the Congress, and before that too their power was nowhere near absolute. And at present, the government is not communist. The one place where the communist party was all powerful until recently was West Bengal. That was due to land reforms they carried out in the 50s, after which the communist party sat back and chilled. Since the rest of India was also by and large socialist, there wasn’t a huge gap in growth. After India’s liberalisation though, it became increasingly clear that the communist party wasn’t delivering, and after trying one moderate communist, they finally voted them out of power last year.

To sum up - there are no governments formed by communist parties in India today, and at the national level too they have very few seats - they are practically irrelevant.