I think it's interesting that Marvel's villains are rarely attached to their heroes on a personal level. The exceptions being the great ones like Loki and presumably Ultron. The result is that the villain conflict is unimportant, so much so that
the villains are rarely actually defeated by the heroes.
Was the movie called Super Pepper or Iron Man 3? I forget. I feel like Pepper has saved the day at least as much if not more than Tony in these movies.
There is nothing good to say about Iron Man 3 - a complete botch of an otherwise great trilogy.
I'd prefer the main, titular character to take down the villain in earnest. Since the movie involves his arc and the villain ties very directly into that arc. Instead, he simply weakens him, allowing a secondary character to swoop in and take care of business while RDJ sits there queuing up for another one-liner.
Just a personal preference. Nice of you to jump straight to assumed misogyny, though

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Pepper is Tony's everything, and his overall arc is very much about his relationship with Pepper and his inability to tinker with that. That is the first problem we're introduced to in IM3, his relationship with Pepper. In order for that arc, the arc of IM3, to be resolved, there had to be a deeper connection than before, one where Pepper could identify with Tony's world, she had to step into that.
It gets better. The thing that made Tony "better" than Killian was basically he had grown beyond selling weapons and had Pepper. The most visceral way to illustrate that is if Pepper, the thing Killian doesn't have, is what beats him. Tony's last words to Killian "She was already perfect." are thematically a summon in this case. Pepper is his victory, not out weaponing another weapon guy.
It gets even better. Tony's main storyline is about his tinkering, and how he needs to stop using that to solve emotional problems and embrace that as his superpower instead of the results per se. This is why he needs to blow up the armors at the end, because they are not his superpower, him being The Mechanic is his super power. Pepper, ready for adventure, ready to take charge and armed with an Iron Man repulsor and random Stark missiles laying on the ground is absolutely a result of Tony's tinkering, mostly on an emotional level. Plus it's a callback to IM1 when Pepper defeated Stane for Tony, and everyone loved that.
They made the right call based on the story. Now I do agree the movie could have been called "Tony Stark's Life" in order to more accurately describe what was the central focus. So those saying "Iron Man" didn't get enough focus in Iron Man 3, I feel you to a point. That said, Captain America and Thor's first villains defeated themselves, the heroes just stopped their plans. Captain America didn't defeat Pierce, or Bucky actually. Thor beat Malekith, I think, without Jane actually helping with the punching, she just hit the buttons, so that's something I think, and of course Iron Man and Rhodey actually did defeat Whiplash and Hulk definitely soloed Abomination. It seems the only time the heroes actually beat the villains themselves was in the least liked MCU films. Crazy. GotG may be an exception, because Quill was directly involved but the film is getting great marks. Perception is a funny thing. It feels like this was the first time a supporting characters took out the villain, but it's far from it.