Iran itinerary question

Save that for another decade.

I would ask the question on a non Europe-centric travel forum like Lonely Planet, etc where the travelers aren't primarily from the US. Keep in mind how politics has shaped an average American's view of Iran for decades. I doubt you'll find many folks here who have traveled there and could give you solid advice.

I have been to Iran, to all three of the cities you want to visit. I do think, with only one week for the trip, you had best leave Teheran for another time. Isfahan and Shiraz are more beautiful and with only a day or two in Teheran I can’t see how much you would learn about the “history, culture and politics”.

I have friends from Iran that can't go back to that country or they would likely be executed or imprisioned.

Sure, some Americans have gone to Iran, and some make it back, while a few are thrown in jail.
I love ancient history and would love to visit Iran, but would never go there now.

I agree that asking on other more global forums would be advantageous. Lonely Planet and TripAdvisor. TripAdvisor tends to offer input by locals as well as recent and well versed travelers. Lonely Planet often has a more intrepid traveler base.
There are also tours to consider, but I expect few offer just a week.
Not all here carry only an American passport. Know the risks and advantages for you specific circumstances.

There were a couple of Americans in our group, but when asked they just said casually that they were Canadian. Not at Immigration, of course and as this was about 15 years ago, their American Passport did not, apparently, present a problem. If ever you are ”allowed” to go to Iran, do not miss Persepolis. That alone is worth the journey.

You may be aware that Rick Steves visited Iran a few years ago and made a TV special about it.

You can view it here: https://www.ricksteves.com/watch-read-listen/video/travel-talks/iran

I don't know if it will help answer your question, but if you haven't seen it, it's worth watching.

Tours that I've considered spent only minimal time in Tehran, any way, even though they were longer tours. If you have your visas in order and find flight options from Dubai that skip Tehran, then I would go ahead and get to your preferred destinations as quickly as possible.