They also can't just let the US destroy their entire navy and air force and just shrug their shoulders with a "well, what can you do?"

Sure. What happened the last time Israel made Iran look hbad?
theintercept.com - Iran attack israel drones missiles

They launched loads of missiles and drones and most were shot down with zero damage. But then what?

Iran “has achieved all its goals, and in our view the operation has ended, and we do not intend to continue,” Mohammad Bagheri, chief of staff of the Iranian armed forces, said over the weekend. Still, he cautioned, “If the Zionist regime or its supporters demonstrate reckless behavior, they will receive a decisive and much stronger response.”

Sure, Jan.

Iran's got one of the most powerful militaries in the region (behind Israel, maybe Egypt).

I'm sure there's some team in Quito that can boast of being Ecuador's finest hockey team. But when you drop the gloves in the NHL, guess what? You dropped the gloves in the NHL.

You keep hyping Iran and their capabilities. Let's see what their Order Of Battle looks like, shall we?

Let's start with their Navy. I trust you'll find this source reasonable:
oni.navy.mil: PDF document

The IRGC naval strategy is an extension of Iran’s national
defense strategy, which seeks to, deter a maritime
attack if possible, rapidly escalate if deterrence fails, and
wage a protracted war if necessary. Fundamental to this
strategy is the exploitation of geography and the use of
asymmetric doctrine to combat a technologically superior
force.

Translation: This means they lack the means to go toe-to-toe with a true blue water Navy so they lean on "asymmetric" means (read: terrorist or pirate-like tactics on the water) to get the job done. They also count on fighting in home waters.

. The doctrine manifests itself as hit-and-run style,
surprise attacks, or the amassing of large numbers of
unsophisticated weapons to overwhelm the enemies’
defenses. The amassing of naval forces is often described
as a swarm of small boats, and is essentially similar to
the human wave attacks Iran’s ground forces used in the
Iran-Iraq War.

Translation: Lots of dude in speedboats. The speedboats will have RPGs and a machine gun on board, maybe a Harpoon knock-off. That's about it.

Their "Capital Ships" are in the weight class of a more heavily armed version of a USCG Cutter. They also employ some North Korean-built submarines and some legacy Soviet boats. Aviation wise their Navy doesn't have much; they retrofitted some old Bell helicopters to carry missiles.

How about their Air Force? (info on their Army is limited)
bing.com: Search - Microsoft Bing

The Iranian air force on paper is one of the biggest air arms in the world. Its order of battle includes around 350 fighters, more than twice as many as the Royal Air Force possesses.

Wow, that's impressive! Or is it?
The air force’s squadrons fly American-made F-14s, F-5s and F-4s dating from the 1970s, some 1980s-vintage MiG-29s and Sukhoi fighter-bombers and a few J-7s that the Islamic Republic bought from China during the 1990s.

Iran’s only recent acquisitions are locally-made, reverse-engineered copies of the F-5.

The F-5 was a nice, lightweight and cheap fighter. Terrific airframe for...1959. Lacking AWACS support in a meaningful way it won't fare so well against a modern Air Force.

They'd ask for (and probably receive) permission from Iraq to cross the Shatt al Arab and enter Kuwait over land and engage with U.S. forces there.

LOL. And we'd drop propaganda leaflets of the Highway Of Death in Kuwait circa 1991.
en.wikipedia.org - Highway of Death