Again. Try reading my posts from other threads. That would be helpful, but for your sake i'll explain.
First, you can't compare a one on one fight to an invasion where a village is your responsibility.
During her Kabuto fight, all the three Sannins were handicapped. Jiraiya (drugged), Orochimaru (Armless) & Tsunade (Rusty & Blood Phobia) Kishi can't just show to us Sage mode and Hydra Justu that time because the Sannin will be overpowered and will lack development later on.
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Still, Kabuto praised her power even at her fallen state.
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Did you see, she was even holding her own in an elite jounin on Kakahi's level despite of being rusty.
Minato and Tsunade's administration were faced into an invasion, but with different invaders. Comparing Minato and Tsunade is not right. If Minato was on Tsunade's position, many people would have died. The attack of the Kyuubi can be anticipated as it doesn't use techniques, only massive chakra blast which minato teleported somewhere else.
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On the other hand, Pain is human/shinobi who possesses the rinnegan. He knows variety of justus which Tsunade/Konoha was in the process of learning. Pain's technique is not a blast rather a gravitational pull. How could have minato teleported such attack?
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And I don't think Minato would have fought Pain head on. There are five shinobis plus Konan roaming around Konoha. Even he's fast he wouldn't be able to defeat one body easily. If he fought one pain, deva could prepare Shinra Tensei on the air.
Also, the third Hokage is there to give assistance. So basically two Kages are fighting that's why Minato wasn't afraid to risk his life because he knew the third was there, as oppose to Tsunade. Danzo didn't even help her, even so Danzo isn't the person to trust most.
As with Tsunade, we don't know how well she could have done in Minato's postion, but with the help of the Third the success rate is huge. We still don't know what she's really capable of. She's a senju & a uzumaki after all which means she can be proficient with seals like Minato.
There
Countless opportunities?
I haven't seen anyone from the Kages went out for a Mission? aren't they the ones giving orders for mission? If the Hokage went out for missions the village will be vulnerable for attacks. Common Sense.
Beating Madara, Kyuubi or the Kin Gin Bros weren't missions at all. The Kages were forced to fight them. As for Tsunade, Pain was the greatest threat where she had the opportunity to fight, but Pain flew and nuke the village. You can't blame her for that. This is a shonen manga and the bests are saved for last that's why we haven't seen her fight all out and she's the last remaining sannin. I'm sure that's why the naruto and sasuke fight will be the last fight we'll see in this manga.