Your logic is flawed. We don't need a ground invasion, we have a blockade that is working just fine.
If we invaded, we'd bring the Kurds, and the Gulf states. We'd also get the 570,000 man Artesh.
All against the 125,000 IRGC. Not "sacrificing" many at all. In Iraq we lost about 4,000 no where near a million.
We'd do even better in Iran.
It's not about how good, or how bad is your blockade. It's about your readiness and preparedness to absorb damage and suffer casualties. What if (not that big "if") your blockade doesn't work and the Kurds are decide to fight against you, and Gulf states (including Israel) refused to die for your ambitions, what if Iran find a countermeasures against your blockade both economically (other trade lanes) and military - like unmanned little silent submarines with AI to find US ships in the certain region? What if you face the choice - 1) alleviate; 2) start a ground invasion with possible further nuclear escalation; 3) to use tactical nukes (with the risk of escalation and total devastation of the region, with its fragile infrastructure).
If your nukes are off the table, then Russian and Chinese nukes (at least tactical) are definitely on the table.
Extermination is not worth the risk.
You aren't free if you are dead. Playing with nuclear weapons only gets them exterminated.
We are going to give them freedom from the vicious ayatollahs and the IRGC.
Celebrations have erupted across Iran as citizens cheer on the US and Israeli missile strikes that targeted the regime, according to Middle Eastern outlets.
nypost.com
Aren't you an American? Aren't you ready to die for your freedom? Aren't they fanatics who do want to die for what they believe is their religious duty? C'mon, perception of Iranians (and other nations) as genetic slaves and subhumans is not only racist, it's simply wrong and misleading.
So, let's assume that they are ready to die for their freedom, and as they wish, Russia and China are ready to help them either to keep Americans away (if America f#ck off after Iran acquire nukes), either die with honour and take as many Americans with them as it will be possible (but no more than 30% of total US population), if they don't.
In this situation the USA will face simple choice:
1) F#ck off and don't fight Iran;
2) Fight Iran and have Middle East destroyed and some American cities with it (suffering terrible, but survivable losses);
3) Fight Russia and China simultaneously and suffer virtual annihilation.
If you don't choose 2, it definitely means that you won't choose 3, too.