" that the US can always escalate the conflict and pursue a ground war. "
You seem to be stuck on repeat with "don't understand, don't understand, don't understand". Yet it seems to me that it is you who got sucked into some bizarro understanding of war being fundamentally an annihilation contest between the two parties involved. This very shallow understanding is now somewhat widespread in the blogosphere and pushed by, again, shallow types like Stephen Miller. Claims like "total destruction and capitulation was the default strategy of war for millenia" are just not true. It happened sometimes, but quite often also not, because warring parties always have some limits to their effort, be it ideological, economic or political limits. And this was no less true in Antiquity than today.
Outside the bizarro "total destruction" corner, war between organized states has been understood primarily as a continuation of politics, with the goal to make your enemy do something that they don't want to. Even the Mongols you mentioned usually gave a besieged city an option to surrender, because their primary goal wasn't simply to kill, but to conquer and rule.
Yes, there are exceptions (Carthago delenda est), but these exceptions aren't the historical rule.
Let us look at the situation in Iran now.
The US seems to want something from Iran. It is not very clear what, but probably free movement of ships through Hormuz, nuclear disarmament and maybe even regime change.
It also does NOT want to genocide the Persians out of existence. While doable, it would carry a heavy reputational penalty and cause significant friction back at home. Not even Trump wants to add tens of millions of civilian lives to his conscience, hence WMDs are out of question.
A ground invasion is thinkable, but I am much less persuaded about its efficiency than you are. As you yourself say, this has a risk of turning into a forever war and the US isn't equipped, mentally nor doctrinally, to fight forever wars.
Which means that you likely won't get what you want from the current Iranian leadership by the sort of military means you can feasibly use against them, and that is not a victory.
Please give me a plausible scenario in which the current US is capable of winning a ground war against Iran in the presence of all the current political limitations, which are quite fundamental. You can't.
Ultimately it does not matter if you can't win because you cannot muster the political will to engage in a costly war, or if you can't win because you run out of Tomahawks (both are correlated, btw). It is still an inability to win, which is obviously detrimental to the US imperial standing.