Trump said he doesn’t want regime change in Iran. That’s misleading. He doesn’t want the regime to change quickly.
If Iran’s nightmare government suddenly collapsed it would bring total chaos as outlying Arab/Muslim nations would surge in like a tsunami in the attempt to be the one that takes over. They’d fight each other as a matter of course and the ordinary citizens of Iran would flee the carnage, pouring into Saudi Arabia and Iraq where they would find themselves unwelcome because they’re Shiites and all the rest are Sunnis. While they don’t hate each other, they don’t love each other either and meanwhile the Chinese, those lovable, irrepressible snatchers of every possible advantage to dominate, would be backing all the invaders to be certain that the winner is deeply indebted to them.
Nothing would be solved, Iran’s sudden collapse would just create a much bigger mess that could involve the entire Middle East. Which is why the US has an absolutely massive naval presence in the immediate area worthy of a World War II Hollywood movie to prevent such an invasion and develop a slow, controlled collapse.
It’s pretty sure that the US doesn’t want the old Shah regime back again. Possibly but much more likely in my opinion will be some sort of protectorate or consortium of specific Middle East nations to manage the country OR outright occupation of Iran by the US. This latter may not seem possible today but that view can change. It makes sense, look what the US just accomplished with Greenland in the name of National Security and then imagine the military benefits after the US leaves NATO, which is another little shocker coming up.