The army’s rapid deployment has been eased by the fact that the US hasn’t fought an opponent with a worthy armed force in conventional war in quite some time. You say if the Marines weren’t the first into Iraq/Afghanistan/etc, then obviously the idea that they’re the expeditionary unit is useless.
But the reality is that the army didn’t fight those wars by parachuting in a bunch of guys using their rapid reaction light forces either. In all wars the US has fought recently, they’ve had ample time to ramp up, establish a supply chain, and get sorted out before attacking. This suits the army’s style.
If something oh-shit-for-real-scary happens, something that actually challenges the US military, the marines as a rapid reaction force would be more useful. Their logistical chain is smaller, leaner, and requires less in the way of support like functional, safe, long runways for the airforce to deliver assloads of supply. They integrate their own light armor and heavy weapons much better than the army light and airborne divisions, while being much faster to deploy and with a smaller supply train than the medium or heavy divisions.
When you have the luxury of using your giant military, network of allies, safe build up zones, and plenty of time against half-ass third world militaries, it doesn’t really matter who you send in.
If you want a sustainable quick response, you send the marines. People talk about how the marines can’t sustain the fight as long as the army - but if we’re talking about comparing parachuting in airborne divisions across the world, their staying power is at least an order of magnitude less. I don’t seriously think we’ll see a major actual parachute operation ever again. Air-mobile, yes, but helicopters have a limited range and the army can’t land anywhere in the world with them - they rely on safe areas for the air force to transport them to, which might not always be available. The marines are capable of bringing their own integral supply train into hostile territory quite a bit more aggressively, as well as having mobile bases all of the world.
TLDR version: In a world where the US has lots of time and bases everywhere to build up to beat up half-ass militaries, it doesn’t matter who you send in. If challenging shit actually went down, and you needed to send in a rapid reaction force halfway across the world, you go Marines.