I find it interesting how people claim, Tsunade should have fought Pein when he started attacking the village. But they forget that considering the SA was made of 80 thousand soldiers from 6 lands that averages out to 13k shinobi who are chuunin rank and above. That doesn't even factor in the civillians who live within Konoha. Yet Tsunade was supposed to find 6 men among that many people with no indication of what they looked like, while having the information that they were being controlled and were not the threat themselves? Is that seriously the well formulated argument you wish to use?
Healing via Katsuyu while having her shinobi, shinobi of the strongest village in the world at that time, protect the village seems like the way to proceed. Then there was a kage level ninja who didn't even bother to help defend the village, and worked behind her back to undermine her plans in progress. Which certainly speaks towards Danzo's own idiocy as he was unaware that Pein could read minds and pick off Naruto from Mount Myobokou at any time he pleased after he crushed the leaf and Naruto would have no support in that fight. There is honestly, no scenario that could have ended better given the conditions Tsunade faced.