At any rate (not going to quibble over the past structure) Iran is at the moment essentially a military dictatorship. No one has seen the new Ayatollah and it's entirely possible he was killed in the first strike that took out Khamanei.

Iran has always been a military dictatorship. As noted in the article posted above, the IGRC has always been the power behind the throne, supportive of the fundamentalist theocratic state and playing kingmaker (and enforcer) to cleric who holds the head of state position. Killing any given mullah - or even large numbers of mullahs - isn't changing anything.

That doesn't mean things might not change in the future, but even if the son was also killed in the initial attacks, we're not causing any material changes in the regime through our operations so far. We're blowing through tens of billions of dollars of military equipment and materiel, specifically including strategically critical anti-missile equipment that will take us years to replenish, on a course that (for now) will just have us come out the other side with essentially the same Iranian government we started with.

That's....not good. We're being operationally successful, and strategically failing:

The war in Iran has reaffirmed two truths. One is that the United States is blessed with the most professional and effective military in the world. The men and women of the American armed forces can conduct missions of almost any size with formidable competence, from special operations to seize a rogue-state president to a large-scale war. The other truth is that the Trump administration, when it comes to strategy, is incompetent.

Strategy is about matching the instruments of national power—and especially military force—to the goals of national policy. The president and his team, however, have not enunciated an overarching goal for this war—or, more accurately, they have presented multiple goals and chosen among them almost randomly, depending on the day or the hour. This means that highly effective military operations are taking place in a strategic vacuum.

theatlantic.com - Iran strategy victory disease

It's not clear what the goal is that's worth burning through so much of our military capabilities. We're destroying a lot of Iranian material, but we're destroying a lot of our own material to do it. Hard to see what goal that furthers, since they'll be able to replace their equipment over time (just as we'll be able to replace our own). Sure, they suffer from an intermediate-term lack of access to that equipment - just as we'll suffer from an intermediate-term lack of access to that equipment. Using up a massive amount of the US' anti-missile systems and protective capacity on Iran doesn't seem like an effective use of that resource, especially in a world where that's a major threat profile and where we might prefer to have those resources available to deploy in other theaters (like, IDK, defending assets and allies in the Pacific theater against Chinese missiles and drones).