The Shah’s son has stated that he is seeking not the establishment of another ruling monarchy, but to serve as essentially a figurehead, no different than Queen Elizabeth II of England, and he supports democracy for Iran.
After seeing how everything ended for his father, that is the wisest decision he could make.
As for Iranian society not being ‘truly free’, riddle me this Batman: was Iranian society more free or less free before the Ayatollah Khomeini came prancing back to Iran?
As for life being better under the Shah than under the mullahs — A couple of years ago I met a woman who lived through both regimes. Someone in our group asked her if she would have liked to see the mullahs deposed and the Shah's son in power. She said no, not really. While of course, the Shah[s regime was more secular, he was still a dictator. And yes, he did persecute and kill anyone he perceived as an enemy — not just the radicals.
And by the way, there are “experts” out there who say that even with a regime change, Iran will still pursue the development of nuclear weapons. I don't see the advantage of trading one authoritarian government for another.