Interservice cooperation is one thing. Throwing people together, regardless of how it looks good in a movie, just doesn't work. One more bird wouldn't have changed those odds at all.
It went way beyond the interservice 'Everybody has to get their slice of the pie' problem. My understanding of the plan from open-source materials that came out much later is that essentially they intended to use in-country assets (Who we would have doubtless left high and dry afterward, so what are the odds that plan was actually secure? Foreigners may hate their own regime, but they aren't stupid, and these would be the guys who watched us sell out our pal the Shah only a short time before) as well as raiders to bust in and rescue the hostages. Assuming the raiders and at least some of the hostages survived that adventure, they were then supposed to get to the freshly-seized PZ in a stadium (Needless to say, seizing it too early would tip the hand, so 'Split-second timing' would be an understatement of the requirement; have you ever tried to navigate through the streets of a Mideastern city on a split-second basis on a normal day, let alone one where all Hell is breaking loose?), all of this supposedly covered by orbiting gunships.
It would have basically required the Iranians to spaz in place for three hours in total paralysis. However numerous and whatever their other faults may be, the Revolutionary Guard is not known for spazzing out or showing the slightest reluctance to fling themselves into gunfire as long as they have some chance of dying in battle against infidels and killing some of the foreign devils to boot. The gunships would have run out of ammo long before the Iranians ran out of Revolutionary Guards with weapons.
Probably would've ended up killing thousands of Iranians (Which is good as far as it goes) at the cost of most of the raiding force, the majority of their AC, most of the hostages, and then ended with possibly a couple of the extraction aircraft getting out loaded.
